Mental math check: 1% of $3,250 is $32.50, and 6 \times 32.50 = 195.
She earned $195 in commission.
Check:195 \div 3{,}250 = 0.06 = 6\% ✓
Tip: Find 1% (move the decimal two places left) and multiply by the percent — it's a fast way to do percents without a calculator. Be careful not to use 0.6 (which is 60%).
Question 3 of 36
No calculator
A jacket regularly sells for $80. It is on sale for 25% off. What is the sale price?
Hint
25% is the same as \tfrac{1}{4}. How much is taken off, and what is left?
One-step version: paying 75% of the price, 80 \times 0.75 = 60.
The sale price is $60.
Check:\tfrac{1}{4} of $80 is $20, and \$60 + \$20 = \$80 ✓
Tip: "25% off" means you pay 100\% - 25\% = 75\%. Multiplying by 1 - \text{rate} gives the sale price in one step and keeps you from choosing the discount amount by mistake.
Question 4 of 36
No calculator
During a holiday sale, a department store takes 35% off every winter coat. Lena picks a coat with a tag price of $120. How much will she pay for it before tax?
Hint
Find 35% of $120, then decide what to do with that amount. Or find what percent of the price you still pay.
Step-by-step solution
Find the discount: 35\% of $120. 0.35 \times 120 = \$42
By hand: 10\% of 120 is 12, so 30\% = 36; 5\% = 6; 36 + 6 = 42.
Subtract the discount from the regular price: \$120 - \$42 = \$78
Shortcut: 35% off means you pay 100\% - 35\% = 65\%: 0.65 \times 120 = \$78.
Tip: "Percent off" gives you the discount, not the price. Either subtract the discount or multiply by the percent you still pay (1 - \text{rate}). The sale price must be less than the original, and for any discount under 50% it must be more than half of the original.
Question 5 of 36
No calculatorFill in
A real estate agent earns a 3% commission on the price of each home she sells. She sells a home for $215,000. How much commission does she earn?
$
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Write 3% as a decimal. Be careful: it is not 0.3.
Step-by-step solution
Change the percent to a decimal: 3\% = \frac{3}{100} = 0.03
Multiply by the sale price: 0.03 \times \$215{,}000 = \$6{,}450
By hand: 1\% of 215,000 is 2,150 (move the decimal point two places left). Then 3\% = 3 \times 2{,}150 = 6{,}450.
She earns a commission of $6,450.
Check:\$6{,}450 \div \$215{,}000 = 0.03 = 3\% ✓ Estimate: 3% of about $200,000 is $6,000, close to $6,450 ✓
Tip: Find 1% first by moving the decimal point two places left, then multiply. This mental-math method avoids the most common error, writing 3% as 0.3, which would make the commission $64,500, ten times too big.
Question 6 of 36
No calculator
Jordan's dinner bill is $46.00. He wants to leave an 18% tip. What is the total he will pay, including the tip?
Hint
Find 18% of $46, then remember the question asks for the total.
Step-by-step solution
Change 18% to a decimal: 18\% = 0.18.
Find the tip: 0.18 \times \$46 = \$8.28
By hand: 10\% of 46 is 4.60; 8\% is 8 \times 0.46 = 3.68; 4.60 + 3.68 = 8.28.
Add the tip to the bill: \$46.00 + \$8.28 = \$54.28
Shortcut: 46 \times 1.18 = 54.28.
Jordan will pay $54.28 in total.
Check: The tip is a bit less than 20% of $46, which is $9.20; $8.28 is a bit less ✓ so the total $54.28 is reasonable.
Tip: Read the last line of the question: "tip" and "total" are different answers, and both usually appear among the choices. Multiplying by 1 + \text{rate} (here 1.18) gives the total in one step.
Question 7 of 36
Carlos puts $2,400 in a savings account that pays 3.5% simple interest per year. How much interest will he earn in 18 months?
Hint
Use I = Prt (on the formula sheet). The time t must be in years.
Step-by-step solution
Identify the values: P = 2{,}400, r = 3.5\% = 0.035.
Change months to years: t = \frac{18}{12} = 1.5\text{ years}
Apply the formula: I = Prt = 2{,}400 \times 0.035 \times 1.5 = 126
He will earn $126 in interest.
Check: One year of interest is 2{,}400 \times 0.035 = \$84; half a year is $42; 84 + 42 = 126 ✓
Tip: In I = Prt, the rate is per year, so time must be in years: divide months by 12. Also note the question asks for the interest, not the account balance ($2,526).
Question 8 of 36
Fill in
The price of a pair of headphones dropped from $250 to $210. What was the percent decrease?
%
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Find the amount of the drop, then divide by the original price.
Step-by-step solution
Amount of change: 250 - 210 = 40
Divide by the original price: \frac{40}{250} = 0.16
Change to a percent: 0.16 \times 100\% = 16\%
The price decreased by 16%.
Check: 16% of $250 is 0.16 \times 250 = \$40, and 250 - 40 = 210 ✓
Tip: Percent change always divides by the original value. Dividing by the new price (40 \div 210 \approx 19\%) is the most common error on this kind of question.
Question 9 of 36
A store buys a backpack for $36 and marks up the price by 40%. Later, the backpack is put on sale for 25% off the marked price. What is the sale price?
Hint
Do the percents one at a time. The 25% is taken off the marked price, not the store's cost.
Tip: Successive percents multiply: 1.40 \times 0.75 = 1.05, so the sale price is 5% above cost — not 15% (which you'd get by subtracting 40\% - 25\%). Each percent applies to the price at that moment.
Question 10 of 36
Drop-down
A family's restaurant bill is $64 before tax. The sales tax is 7%, and they leave a 20% tip on the pre-tax amount.
Choose the correct answer for each blank.
The sales tax is , and the total they pay, including tax and tip, is .
Choose an answer from each menu.
Hint
Both the tax and the tip are percents of the same base: the $64 pre-tax bill.
Step-by-step solution
Tax: 0.07 \times 64 = \$4.48
Tip (on the pre-tax amount): 0.20 \times 64 = \$12.80
Total: 64 + 4.48 + 12.80 = \$81.28
Shortcut: both percents use the same base, so 64 \times (1 + 0.07 + 0.20) = 64 \times 1.27 = 81.28.
Tip: Percents of the same base can be added (7% + 20% = 27%). If the tip were figured on the after-tax total, the base would change and the total would be $82.18 — so always read which amount the tip is based on.
Question 11 of 36
No calculatorSelect all
A gym raises its monthly fee, p, by 15%. Select all the expressions that equal the new monthly fee.
Select all that apply.
Hint
The new fee is the old fee plus 15% of the old fee. What single number can you multiply p by?
Step-by-step solution
The new fee is the original fee plus 15% of it: p + 0.15p.
p + 0.15p ✓ — the original plus the increase.
1.15p ✓ — combine like terms: p + 0.15p = (1 + 0.15)p = 1.15p.
\tfrac{115}{100}p ✓ — \tfrac{115}{100} = 1.15.
0.15p ✗ — this is only the increase, not the new fee.
Tip: An increase of r is the multiplier 1 + r. Testing a simple number for the variable (like 40 or 100) is a quick way to check which expressions are equivalent.
Question 12 of 36
After a 15% discount, a pair of work boots costs $51. What was the original price of the boots?
Hint
The $51 sale price is what percent of the original price? Write an equation with the original price as the unknown.
Step-by-step solution
After 15% off, the customer pays 100\% - 15\% = 85\% of the original price x: 0.85x = 51
Divide both sides by 0.85: x = \frac{51}{0.85} = 60
The original price was $60.
Check: 15% of $60 is $9, and 60 - 9 = 51 ✓
Tip: To undo a percent change, divide by the multiplier. Adding 15% back on (51 \times 1.15 = \$58.65) fails because the discount was 15% of the original price, which is bigger than $51.
Question 13 of 36
Fill in
Keisha borrows $1,800 to repair her car. The loan charges 6% simple interest per year, and she repays everything at the end of 3 years. What is the total amount she repays (the amount borrowed plus interest)?
$
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Use I = Prt from the formula sheet to find the interest. Then answer the question that was asked.
Step-by-step solution
Write the simple interest formula (on the GED formula sheet): I = PrtP = \$1{,}800, r = 6\% = 0.06, t = 3 years.
Find the interest: I = 1{,}800 \times 0.06 \times 3 = 108 \times 3 = \$324
Add the interest to the amount borrowed: \$1{,}800 + \$324 = \$2{,}124
Keisha repays $2,124 in total.
Check: Each year the interest is 0.06 \times 1{,}800 = \$108. Three years: 3 \times 108 = \$324, and 1{,}800 + 324 = 2{,}124 ✓
Tip:I = Prt gives only the interest. If the question asks for the total, balance, or amount repaid, add the principal: A = P + I. Simple interest is the same dollar amount every year.
Question 14 of 36
The population of a small town grew from 12,500 to 14,000 people. What was the percent increase?
Hint
Percent change = \dfrac{\text{change}}{\text{original}} \times 100\%. Which number is the original?
Step-by-step solution
Find the amount of change: 14{,}000 - 12{,}500 = 1{,}500 \text{ people}
Divide by the original (starting) value: \frac{1{,}500}{12{,}500} = 0.12
Change to a percent: 0.12 \times 100\% = 12\%
The population increased by 12%.
Check:12\% of 12,500 is 0.12 \times 12{,}500 = 1{,}500, and 12{,}500 + 1{,}500 = 14{,}000 ✓
Tip: Always divide the change by the value you started from (the "old" value). Dividing by the new value (1{,}500 \div 14{,}000 \approx 10.7\%) is the most common mistake, and it often appears as a wrong answer choice.
Question 15 of 36
No calculatorSelect all
A store marks down every item by 30%. The original price of an item is p dollars.
Select all the expressions that equal the sale price of the item.
Select all that apply.
Hint
The sale price is the original price minus 30% of the original price. What percent of the price is left?
Step-by-step solution
The sale price is the original price minus 30% of it: p - 0.30p = 0.70p. Test each expression.
0.7p ✓ — you pay 100\% - 30\% = 70\% of the price.
p - 0.3p ✓ — original price minus the discount.
p(1 - 0.30) ✓ — the distributive property gives p - 0.30p = 0.7p.
p - 30 ✗ — subtracts 30 dollars, not 30 percent.
0.3p ✗ — this is the discount, not the sale price.
p - 0.03p ✗ — uses 0.03, which is 3%, not 30%.
Correct: 0.7p, p - 0.3p, and p(1 - 0.30).
Check: Try p = 100: the sale price should be \$70. Then 0.7(100) = 70 ✓, 100 - 0.3(100) = 70 ✓, 100(1 - 0.30) = 70 ✓; but 0.3(100) = 30 ✗ and 100 - 3 = 97 ✗. (Note: p - 30 also gives 70 when p = 100. Test a second value such as p = 50: 50 - 30 = 20, but the sale price is 0.7 \times 50 = 35 ✗.)
Tip: Plugging in p = 100 makes percent expressions easy to test, but p = 100 hides the "percent as dollars" error. Check a second value to be sure.
Question 16 of 36
The table shows the Nguyen family's electric bills for four months.
Month
Bill
January
$84
February
$105
March
$91
April
$70
What was the percent change in the bill from February to April?
Hint
Find the two values in the table first. Which month is the starting value?
Step-by-step solution
Read the table: February (the start) = \$105; April (the end) = \$70.
Find the change: 70 - 105 = -35 The bill went down by $35.
Divide by the starting value (February): \frac{-35}{105} = -\frac{1}{3} \approx -0.333
Change to a percent: -0.333 \times 100\% \approx -33.3\%
The bill decreased by about 33.3%.
Check:33.3\% of $105 is about \tfrac{1}{3} \times 105 = \$35, and 105 - 35 = \$70 ✓
Tip: With a table, circle the two values the question names (and ignore the others). The month that comes first in time is the original value, even if it is not the first row of the table.
Question 17 of 36
A shoe store pays $45 for a pair of running shoes. The store marks up the price by 60%. What is the store's selling price for the shoes?
Hint
A markup is added to the store's cost. Find 60% of $45 first.
Step-by-step solution
Find the markup amount: 60\% \text{ of } \$45 = 0.60 \times 45 = \$27
Add the markup to the store's cost: \$45 + \$27 = \$72
Shortcut: a 60% markup means the price is 100\% + 60\% = 160\% of the cost: 1.6 \times 45 = \$72.
Tip: A markup percent is always a percent of the cost (what the store paid). Multiply the cost by 1 + \text{markup rate} to get the selling price in one step.
Question 18 of 36
A tablet has a regular price of $160 at two stores. Store A offers 25% off. Store B offers $35 off. Which store has the lower price, and by how much?
Hint
Find the final price at each store. You can't compare 25% and $35 directly.
Step-by-step solution
Store A: the discount is 0.25 \times 160 = \$40, so the price is \$160 - \$40 = \$120
Store B: the price is \$160 - \$35 = \$125
Compare: \$125 - \$120 = \$5.
Store A is cheaper, by $5.
Check: 25% is one quarter, and one quarter of $160 is $40, which is a bigger discount than $35 ✓ So Store A must be cheaper, by 40 - 35 = \$5.
Tip: To compare a percent discount with a dollar discount, turn the percent into dollars using the actual price. The answer can flip for a different price: on a $100 item, 25% off is only $25, and $35 off would win.
Question 19 of 36
A television regularly costs $250. It is marked 20% off, and at checkout the store takes an extra 10% off the sale price. What is the final price?
Hint
The extra 10% is taken off the sale price, not the regular price. Do one discount at a time.
Step-by-step solution
First discount: 20% off $250. You pay 80%: 0.80 \times \$250 = \$200
Second discount: 10% off the sale price of $200. You pay 90%: 0.90 \times \$200 = \$180
In one step: 250 \times 0.80 \times 0.90 = 250 \times 0.72 = \$180
The final price is $180.
Check: The total discount is \$250 - \$180 = \$70, which is 70 \div 250 = 28\%, not 30%, because the second 10% was taken from a smaller amount ✓
Tip: Successive percents multiply; they don't add. "20% off, then 10% off" is a 28% discount, not 30%. Use the multipliers (1 - r_1)(1 - r_2).
Question 20 of 36
Fill in
Luis deposits $5,000 in a certificate of deposit that pays 4% simple interest per year. How many years will it take to earn $700 in interest?
years
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Put the known values into I = Prt and solve for t.
Step-by-step solution
Start with the formula from the formula sheet: I = Prt
Substitute I = 700, P = 5{,}000, r = 0.04: 700 = 5{,}000 \times 0.04 \times t
Simplify: 5{,}000 \times 0.04 = 200, so 700 = 200t
Divide both sides by 200: t = \frac{700}{200} = 3.5 \text{ years}
It will take 3.5 years (3 years 6 months).
Check:5{,}000 \times 0.04 \times 3.5 = 200 \times 3.5 = \$700 ✓ The account earns $200 each year, and $700 is three and a half years' worth.
Tip: For any "find the missing value" interest question, write I = Prt, plug in what you know, multiply the known numbers together, and divide. Your answer for t is in years if the rate is per year.
Question 21 of 36
The price of a share of stock rose 20% in March and then fell 20% in April. What was the overall percent change from the start of March to the end of April?
Hint
Pick an easy starting price, such as $100, and apply each change in order.
Step-by-step solution
Start with $100 (any starting value gives the same percent).
Check: Using multipliers: 1.20 \times 0.80 = 0.96, and 0.96 = 1 - 0.04 → a 4% decrease ✓
Tip: Successive percent changes multiply; they don't cancel or add. The 20% drop is taken from a larger number ($120), so it removes more dollars ($24) than the rise added ($20).
Question 22 of 36
Fill in
Andre earns a base pay of $500 per week plus a 4.5% commission on all of his weekly sales over $10,000. Last week his total pay was $1,130.
What were his total sales last week?
$
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Subtract the base pay to find the commission. The commission is 4.5% of only the sales above $10,000.
Step-by-step solution
Commission earned: 1{,}130 - 500 = \$630
The commission is 4.5% of the sales over $10,000. Let x = sales over $10,000: 0.045x = 630
Solve: x = \frac{630}{0.045} = 14{,}000
Total sales = the first $10,000 plus the amount over it: 10{,}000 + 14{,}000 = 24{,}000
Tip: Work backwards one layer at a time: remove the flat amount (base pay), undo the percent (divide by 0.045), then add back the threshold. Forgetting the last step gives $14,000, the most common wrong answer.
Question 23 of 36
Fill in
The bar graph shows a food truck's total sales for three years.
By what percent did sales decrease from 2023 to 2024?
%
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Read the two bars the question names. Divide the change by the earlier year's sales.
Step-by-step solution
Read the graph: 2023 sales = \$56{,}400 (the original value); 2024 sales = \$50{,}760.
Find the decrease: 56{,}400 - 50{,}760 = \$5{,}640
Divide by the original (2023) value: \frac{5{,}640}{56{,}400} = 0.10
Change to a percent: 0.10 \times 100\% = 10\%
Sales decreased by 10%.
Check: 10% of $56,400 is $5,640, and 56{,}400 - 5{,}640 = 50{,}760 ✓ (Dividing by 2024's value would give 5{,}640 \div 50{,}760 \approx 11.1\%, which is wrong.)
Tip: Ignore bars the question doesn't ask about (2022 here). The earlier year is always the base of a percent change, whether the change is up or down.
Question 24 of 36
Drop-down
A furniture store buys a sofa for $480 and puts it on the floor with a price tag of $696. Months later, the sofa sells at 25% off the tagged price.
Choose the correct answer for each blank.
The store's markup was of its cost. After the sale discount, the store's profit on the sofa was .
Choose an answer from each menu.
Hint
Markup percent is based on the store's cost. Profit is what the store got minus what it paid.
Step-by-step solution
Markup percent
Markup amount: \$696 - \$480 = \$216
Divide by the store's cost: \frac{216}{480} = 0.45 = 45\%
Profit after the sale
Sale price: 25% off $696, so the customer pays 75%: 0.75 \times \$696 = \$522
Tip: Markup is a percent of the cost, but a sale discount is a percent of the tagged price. Because they use different bases, a 45% markup and a 25% discount do not leave a 20% profit; always compute the dollar amounts.
Question 25 of 36
Erin is choosing between two sales jobs.
Job A: a salary of $2,000 per month
Job B:$1,200 per month plus a 5% commission on her monthly sales
What amount of monthly sales would make the two jobs pay the same?
Hint
How much more does Job A pay before any commission? The commission in Job B has to make up that difference.
Step-by-step solution
Job B starts $800 behind: \$2{,}000 - \$1{,}200 = \$800
The 5% commission must make up that $800. Let s be the monthly sales: 0.05s = 800
Divide by 0.05: s = \frac{800}{0.05} = \$16{,}000
(Equation version: 1{,}200 + 0.05s = 2{,}000 gives the same result.)
The jobs pay the same when monthly sales are $16,000.
Check: Job B pay = 1{,}200 + 0.05 \times 16{,}000 = 1{,}200 + 800 = \$2{,}000, equal to Job A ✓ With more sales than $16,000, Job B pays more.
Tip: For a "break-even" question, set the two pay expressions equal and solve. Dividing by 0.05 is the same as multiplying by 20, a quick mental check: 800 \times 20 = 16{,}000.
Question 26 of 36
Shanice's receipt shows a total of $85.20, which includes 6.5% sales tax. What was the price of her purchase before tax?
Hint
The total is 106.5% of the pre-tax price. Taking 6.5% of the total uses the wrong base.
Step-by-step solution
Let p be the price before tax. The total is the price plus 6.5% of the price: p + 0.065p = 1.065p
Set it equal to the total: 1.065p = 85.20
Divide both sides by 1.065: p = \frac{85.20}{1.065} = \$80.00
The price before tax was $80.00.
Check: Tax on $80 is 0.065 \times 80 = \$5.20, and 80 + 5.20 = \$85.20 ✓
Tip: To undo a percent increase, divide by the multiplier (1 + \text{rate}). Do not subtract the percent of the final amount; the tax was 6.5% of the smaller, pre-tax price.
Question 27 of 36
Fill in
As part of a doctor's health plan, Marcus went from 240 pounds to 207 pounds. What was the percent decrease in his weight?
%
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Find the number of pounds he lost, then divide by his starting weight.
Step-by-step solution
Find the change: 240 - 207 = 33 \text{ pounds}
Divide by the original weight (240 pounds): \frac{33}{240} = 0.1375
Change to a percent: 0.1375 \times 100\% = 13.75\%
His weight decreased by 13.75%.
Check: 13.75% of 240 is 0.1375 \times 240 = 33 pounds, and 240 - 33 = 207 ✓ (Dividing by the new weight gives 33 \div 207 \approx 15.9\%, the classic wrong-base mistake.)
Tip: A percent decrease always uses the starting value as the base, even when the end value is "nicer" to divide by. Estimate first: 10% of 240 is 24 and 15% is 36, so a 33-pound loss must be between 10% and 15%.
Question 28 of 36
A car salesperson earns a commission of 2% on the first $50,000 of her monthly sales and 3.5% on all sales above $50,000. This month her sales were $82,000. What was her commission?
Hint
Split the $82,000 into two pieces: the first $50,000 and the part above $50,000. Each piece has its own rate.
Step-by-step solution
First tier: 2% of the first $50,000: 0.02 \times 50{,}000 = \$1{,}000
Second tier: sales above $50,000 are 82{,}000 - 50{,}000 = \$32{,}000. At 3.5%: 0.035 \times 32{,}000 = \$1{,}120
Add the two tiers: \$1{,}000 + \$1{,}120 = \$2{,}120
Her commission was $2,120.
Check: The answer should be between 2% of $82,000 ($1,640) and 3.5% of $82,000 ($2,870), because part of her sales earn each rate ✓ $2,120 is in that range.
Tip: In tiered ("bracket") problems, each rate applies only to its own slice of the total. Write the slices first and confirm they add up to the total (50{,}000 + 32{,}000 = 82{,}000).
Question 29 of 36
Tomás takes out a $950 loan for a new refrigerator. The loan has 8.4% simple interest per year, and he pays it off in full after 9 months. What is the total amount he pays?
Hint
In I = Prt, the time must be in years when the rate is per year. What fraction of a year is 9 months?
Step-by-step solution
Convert the time to years: t = \frac{9}{12} = 0.75 \text{ year}
Find the interest with I = Prt (formula sheet): I = 950 \times 0.084 \times 0.75 = 79.80 \times 0.75 = \$59.85
Add the interest to the amount borrowed: \$950 + \$59.85 = \$1{,}009.85
Tomás pays $1,009.85 in total.
Check: One full year of interest is 0.084 \times 950 = \$79.80; three-quarters of that is \$59.85 ✓ and 950 + 59.85 = 1{,}009.85 ✓
Tip: An annual rate needs time in years: months \div 12. Using 9 as the time would charge 9 years of interest; a 9-month loan should cost less than one year's interest.
Question 30 of 36
No calculatorSelect all
The price of a concert ticket, p dollars, goes up 10%. A month later, the new price goes down 10%.
Select all the expressions that equal the final price.
Select all that apply.
Hint
The 10% decrease is taken from the increased price, not from p. Write each change as a multiplier.
Step-by-step solution
After the increase the price is 1.1p. The decrease takes 10% of 1.1p, which is 0.11p. So the final price is 1.1p - 0.11p = 0.99p. Test each expression.
0.99p ✓ — the simplified final price.
(1.1)(0.9)p ✓ — multiply by 1.1 for the increase, then by 0.9 for the decrease: 1.1 \times 0.9 = 0.99.
1.1p - 0.11p ✓ — increased price minus 10% of the increased price.
p ✗ — assumes the two changes cancel. They don't, because the 10% decrease is taken from a bigger number.
1.1p - 0.1p ✗ — takes 10% of the original price (0.1p) instead of 10% of 1.1p; it simplifies to p.
1.01p ✗ — this would be a 1% increase; the overall change is a 1% decrease.
Correct: 0.99p, (1.1)(0.9)p, and 1.1p - 0.11p.
Check: Try p = 100: up 10% gives 110; down 10% of 110 is 110 - 11 = 99. Each correct expression gives 99 ✓, while p and 1.1p - 0.1p give 100 and 1.01p gives 101 ✗.
Tip: Equal percent up and down never cancel; the result is always a little less than the start. Multiply the multipliers to find the overall change.
Question 31 of 36
Priya invested $3,200 in an account that pays simple interest. After 2 years 6 months, she had earned $360 in interest. What is the annual interest rate?
Hint
Use I = Prt and solve for r. Write 2 years 6 months as a number of years first.
Step-by-step solution
Time in years: 6 months = \tfrac{6}{12} = 0.5 year, so t = 2.5.
Substitute into I = Prt: 360 = 3{,}200 \times r \times 2.5
Simplify the right side: 360 = 8{,}000r
Solve: r = \frac{360}{8{,}000} = 0.045 = 4.5\%
The annual interest rate is 4.5%.
Check:3{,}200 \times 0.045 = \$144 per year, and 144 \times 2.5 = \$360 ✓
Tip: Rearranged, the formula is r = \dfrac{I}{Pt}. Convert the time carefully: 2 years 6 months is 2.5 years, not 2.6 (there are 12 months in a year, not 10).
Question 32 of 36
Grace wants to earn $810 in interest over 4 years from an account that pays 4.5% simple interest per year. How much money must she deposit?
Hint
This time the unknown is P. Substitute the other three values into I = Prt.
Step-by-step solution
Use I = Prt (formula sheet) with I = 810, r = 0.045, t = 4: 810 = P \times 0.045 \times 4
Multiply the known factors: 0.045 \times 4 = 0.18, so 810 = 0.18P
Divide both sides by 0.18: P = \frac{810}{0.18} = \$4{,}500
Tip: When solving for P, r, or t, multiply the two known factors on the right first, then divide the interest by that product. Watch the decimal: 4.5% is 0.045, not 0.45.
Question 33 of 36
Drag and drop
The table shows the prices of three grocery items in two different years.
Item
2021 price
2024 price
Eggs (1 dozen)
$2.50
$3.40
Milk (1 gallon)
$4.00
$3.70
Bread (1 loaf)
$3.20
$3.60
Drag the correct percent change (from 2021 to 2024) to each item. A positive value is an increase and a negative value is a decrease. Not every value is used.
Eggs
Milk
Bread
Tap a tile, then tap a box to place it.
Hint
For each item: (2024 price − 2021 price) ÷ 2021 price. Keep the sign.
Step-by-step solution
Use percent change = \dfrac{\text{new} - \text{original}}{\text{original}} \times 100\%, with 2021 as the original.
Tip: The same dollar change can be very different percents: eggs rose 90 cents (36%), but bread rose 40 cents (12.5%). Always divide by each item's own starting price, and keep the minus sign for a decrease.
Question 34 of 36
A clothing store sells a jacket for $91. This price includes a 40% markup over the store's cost. How much did the store pay for the jacket?
Hint
The selling price is 140% of the cost. Is 40% of $91 the same as 40% of the cost?
Step-by-step solution
Let c be the store's cost. A 40% markup means the price is the cost plus 40% of the cost: c + 0.40c = 1.40c
Set it equal to the selling price: 1.40c = 91
Divide by 1.40: c = \frac{91}{1.40} = \$65
The store paid $65 for the jacket.
Check: 40% of $65 is 0.4 \times 65 = \$26, and 65 + 26 = \$91 ✓
Tip: The markup percent is based on the cost, which is unknown here. So you can't take 40% of $91. Undo a markup by dividing by 1 + \text{markup rate}.
Question 35 of 36
Fill in
A used car costs $18,000. The dealer offers two ways to pay:
Option 1: pay in cash today and get a 5% discount.
Option 2: pay the full price with a loan at 4% simple interest per year for 3 years.
How much more does Option 2 cost in total than Option 1?
$
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Find the total cost of each option separately: the discounted price, and the price plus all the interest. Then subtract.
Step-by-step solution
Option 1: cash with 5% discount
You pay 95% of the price: 0.95 \times \$18{,}000 = \$17{,}100
Option 2: loan with simple interest
Interest with I = Prt: I = 18{,}000 \times 0.04 \times 3 = \$2{,}160
Total paid: \$18{,}000 + \$2{,}160 = \$20{,}160
Compare
\$20{,}160 - \$17{,}100 = \$3{,}060
Option 2 costs $3,060 more than Option 1.
Check: The difference is the lost discount (0.05 \times 18{,}000 = \$900) plus the interest ($2,160): 900 + 2{,}160 = \$3{,}060 ✓
Tip: When comparing payment plans, find the total each one costs. Here the gap comes from two sources: the discount you give up and the interest you pay. Leaving out either one gives a tempting wrong answer ($2,160 or $900).
Question 36 of 36
A pair of boots was marked 40% off. At the register, Dale also used a coupon for $12 off the sale price. He paid $51 (before tax). What was the original price of the boots?
Hint
Undo the steps in reverse order: first undo the coupon, then undo the 40% discount.
Step-by-step solution
The store did two things in order: (1) took 40% off the original price, then (2) subtracted $12. Undo them in reverse order.
Undo the coupon: the sale price before the coupon was \$51 + \$12 = \$63
Undo the 40% discount. After 40% off, the customer pays 60%, so 0.60 \times \text{original} = 63\text{original} = \frac{63}{0.60} = \$105
Tip: To work backwards through several steps, undo the last step first (like taking off shoes before socks). And undo a percent discount by dividing by the percent you paid (1 - \text{rate}), never by the discount rate.
