A plumber charges a $65 service fee plus $45 per hour of work. Mr. Ortiz's bill was $245. How many hours did the plumber work?
Hint
The $65 fee is paid once, no matter how long the job takes. Remove it before dividing by the hourly rate.
Step-by-step solution
Let h = number of hours. The bill is the fee plus the hourly charge: 65 + 45h.
Set it equal to the total: 65 + 45h = 245.
Subtract 65 from both sides: 45h = 180.
Divide both sides by 45: h = \dfrac{180}{45} = 4.
The plumber worked 4 hours.
Check:65 + 45(4) = 65 + 180 = \$245 ✓
Tip: In a "fee plus rate" problem, subtract the one-time fee first, then divide by the rate. Dividing the whole bill by the rate ignores the fee.
Question 2 of 36
Fill in
A gym charges a one-time $30 joining fee plus $25 per month. Kendra has paid $230 in total so far. For how many months has she been a member?
months
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Write the total as the joining fee plus $25 times the number of months.
Step-by-step solution
Let m = number of months. Total paid = 30 + 25m.
Equation: 30 + 25m = 230.
Subtract 30 from both sides: 25m = 200.
Divide by 25: m = \dfrac{200}{25} = 8.
Kendra has been a member for 8 months.
Check:30 + 25(8) = 30 + 200 = \$230 ✓
Tip: A wrong answer of 9.2 comes from dividing 230 by 25 without removing the $30 fee first. A number of months should usually be a whole number — a decimal is a warning sign.
Question 3 of 36
The sum of three consecutive integers is 87. What is the smallest of the three integers?
Hint
Call the smallest integer n. Consecutive integers go up by 1 each time.
Step-by-step solution
Let n = the smallest integer. The next two are n + 1 and n + 2.
Add them: n + (n + 1) + (n + 2) = 87.
Combine like terms: 3n + 3 = 87.
Subtract 3: 3n = 84. Divide by 3: n = 28.
The integers are 28, 29, and 30.
The smallest integer is 28.
Check:28 + 29 + 30 = 87 ✓
Tip: For three consecutive integers, \text{sum} \div 3 gives the middle number (29). The smallest is one less. Read carefully which one the question wants.
Question 4 of 36
A taxi charges $4.00 to start the ride plus $2.50 per mile. Ellen's fare was $29.00. How many miles did she ride?
Hint
Let m = miles. The $4.00 is charged once; the $2.50 is charged for every mile.
Step-by-step solution
Let m = the number of miles. Cost = start fee + cost per mile × miles, so 4 + 2.5m = 29.
Subtract the start fee from both sides: 2.5m = 29 - 4 = 25.
Divide by 2.5: m = \dfrac{25}{2.5} = 10.
Ellen rode 10 miles.
Check:4 + 2.50(10) = 4 + 25 = \$29.00 ✓
Tip: In "fee plus rate" problems, take away the one-time fee first. Only the amount that is left is divided by the rate.
Question 5 of 36
No calculator
Five more than three times a number is 38. What is the number?
Hint
"Three times a number" is 3n. "Five more than" that means add 5 to it.
Step-by-step solution
Let n = the number. "Three times a number" is 3n. "Five more than" that is 3n + 5.
"Is 38" means equals 38: 3n + 5 = 38.
Subtract 5 from both sides: 3n = 33.
Divide by 3: n = 11.
The number is 11.
Check: three times 11 is 33, and five more than 33 is 38 ✓
Tip: Translate piece by piece. "Five more than A" is A + 5. It is not 5(A), and the 5 is not inside parentheses with n unless the words say "the sum".
Question 6 of 36
Two cell phone plans charge for calls as follows:
Plan
Monthly fee
Cost per minute
A
$20
$0.08
B
$35
$0.05
For how many minutes of calls in a month do the two plans cost the same?
Hint
Write the monthly cost of each plan for m minutes, then set the two expressions equal.
Step-by-step solution
Let m = minutes. Plan A costs 20 + 0.08m. Plan B costs 35 + 0.05m.
Set the costs equal: 20 + 0.08m = 35 + 0.05m.
Subtract 0.05m from both sides: 20 + 0.03m = 35.
Subtract 20 from both sides: 0.03m = 15.
Divide by 0.03: m = \dfrac{15}{0.03} = 500.
The plans cost the same at 500 minutes.
Check: Plan A 20 + 0.08(500) = 20 + 40 = \$60; Plan B 35 + 0.05(500) = 35 + 25 = \$60 ✓
Tip: Be careful with decimal division. 15 \div 0.03 is the same as 1500 \div 3 = 500 (move both decimal points two places).
Question 7 of 36
Fill in
The rectangular garden below has a perimeter of 54 feet. Its length is 3 feet more than twice its width.
What is the length of the garden?
feet
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Perimeter of a rectangle = 2(\text{length}) + 2(\text{width}). Solve for w first, then find the length.
Check:2(19) + 2(8) = 38 + 16 = 54 ft ✓ and 19 = 2(8) + 3 ✓
Tip: The variable is usually the width, but the question asked for the length. The trap answer is 8. Always finish by answering exactly what was asked.
Question 8 of 36
A jacket is on sale for 20% off the original price. The sale price is $68. What was the original price?
Hint
If 20% is taken off, what percent of the original price do you still pay? Write that as a decimal times p.
Step-by-step solution
Let p = original price. A 20% discount means you pay 100\% - 20\% = 80\% of p.
Equation: 0.80p = 68.
Divide both sides by 0.80: p = \dfrac{68}{0.80} = 85.
The original price was $85.
Check: 20% of $85 is 0.20 \times 85 = \$17, and 85 - 17 = \$68 ✓
Tip: The discount is a percent of the original price, not the sale price. That is why adding 20% of $68 back on ($81.60) is wrong. Set up (\text{percent paid}) \times p = \text{sale price} and divide.
Question 9 of 36
Two trucks leave the same warehouse at the same time and drive in opposite directions on a straight highway. One averages 55 mph and the other averages 65 mph. After how many hours will the trucks be 300 miles apart?
Hint
Use d = rt for each truck. The distance between them is the sum of the two distances.
Step-by-step solution
Let t = hours. Using d = rt: truck 1 goes 55t miles and truck 2 goes 65t miles.
Driving in opposite directions, the distance between them is the sum: 55t + 65t = 300.
Combine like terms: 120t = 300.
Divide by 120: t = \dfrac{300}{120} = 2.5.
They will be 300 miles apart after 2.5 hours.
Check:55(2.5) = 137.5 miles and 65(2.5) = 162.5 miles; 137.5 + 162.5 = 300 ✓
Tip: Moving apart (or toward each other), add the speeds. Moving in the same direction, subtract them.
Question 10 of 36
Drop-down
The formula F = 1.8C + 32 converts a temperature in degrees Celsius (C) to degrees Fahrenheit (F). A thermostat is set to 77°F.
Select the value that makes the statement true.
The thermostat setting in Celsius is °C.
Choose an answer from each menu.
Hint
Substitute 77 for F (not for C), then solve the two-step equation.
Step-by-step solution
The temperature 77 is in Fahrenheit, so substitute it for F: 77 = 1.8C + 32.
Subtract 32 from both sides: 45 = 1.8C.
Divide by 1.8: C = \dfrac{45}{1.8} = 25.
The setting is 25°C.
Check:1.8(25) + 32 = 45 + 32 = 77 ✓
Tip: Before substituting, match each given number to its letter. Here 77 goes with F. Then undo the operations in reverse order: subtract 32 first, then divide by 1.8.
Question 11 of 36
Fill in
A community theater sold 150 tickets for one show. Adult tickets cost $12 and child tickets cost $7. Ticket sales totaled $1,465. How many adult tickets were sold?
adult tickets
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Let a = adult tickets. Then the number of child tickets is 150 - a. Write one equation for the money.
Step-by-step solution
Let a = adult tickets. Then child tickets = 150 - a.
Money from adults: 12a. Money from children: 7(150 - a).
Equation: 12a + 7(150 - a) = 1465.
Distribute: 12a + 1050 - 7a = 1465.
Combine like terms: 5a + 1050 = 1465.
Subtract 1050: 5a = 415. Divide by 5: a = 83.
83 adult tickets were sold (and 150 - 83 = 67 child tickets).
Tip: "When do they cost the same?" always means: set the two cost expressions equal. For fewer miles MoveRite is cheaper; for more miles Haul-It is cheaper.
Question 13 of 36
No calculator
The angles of a triangle measure x^\circ, 2x^\circ, and (x + 20)^\circ. What is the measure of the largest angle?
Hint
The three angles of any triangle add up to 180^\circ. After you find x, find all three angles.
Step-by-step solution
The angles of a triangle add to 180^\circ: x + 2x + (x + 20) = 180.
Combine like terms: 4x + 20 = 180.
Subtract 20: 4x = 160.
Divide by 4: x = 40.
Find each angle: x = 40^\circ, 2x = 80^\circ, x + 20 = 60^\circ.
The largest angle measures 80^\circ.
Check:40 + 80 + 60 = 180 ✓
Tip: Solving for x is often not the last step. Reread the question to see which quantity it asks for.
Question 14 of 36
Marcus bought a vacuum cleaner. With 6% sales tax, he paid $227.90. What was the price before tax?
Hint
The total is the price plus 6% of the price. Write that as one multiplication, 1.06p.
Step-by-step solution
Let p = price before tax. Tax is 0.06p, so the total is p + 0.06p = 1.06p.
Write the equation: 1.06p = 227.90.
Divide by 1.06: p = \dfrac{227.90}{1.06} = 215.
The price before tax was $215.00.
Check:6\% of $215 is 0.06 \times 215 = \$12.90, and 215 + 12.90 = \$227.90 ✓
Tip: The tax is 6% of the original price, not of the total. That is why you divide by 1.06 instead of taking 6% off $227.90.
Question 15 of 36
Fill in
Jen leaves home and walks along a trail at 4 miles per hour. Thirty minutes later, her brother leaves from the same spot and bikes along the same trail at 12 miles per hour.
How many minutes after her brother leaves will he catch up to Jen?
minutes
Type your answer in the box. Fractions like 3/4 are fine.
Hint
When he catches her, they have gone the same distance. Jen has been moving half an hour longer than her brother.
Step-by-step solution
Let t = hours the brother rides. Jen has walked half an hour longer: t + 0.5 hours.
They meet when the distances are equal: 12t = 4(t + 0.5).
Distribute: 12t = 4t + 2.
Subtract 4t: 8t = 2, so t = \dfrac{2}{8} = 0.25 hour.
Convert to minutes: 0.25 \times 60 = 15 minutes.
He catches up 15 minutes after he leaves.
Check: in 0.25 hour the brother rides 12(0.25) = 3 miles. Jen walks for 0.75 hour: 4(0.75) = 3 miles ✓
Tip: Write 30 minutes as 0.5 hour so the units match the speeds (miles per hour). Convert back to minutes only at the end.
Question 16 of 36
A rule of thumb says that the temperature T in degrees Fahrenheit can be estimated from the number of times N a cricket chirps in one minute:
T = \frac{N}{4} + 37
On an evening when the temperature is 65°F, how many times per minute would a cricket be expected to chirp?
Hint
The temperature is the output. Put 65 in for T, then undo the +37 and the division by 4.
Step-by-step solution
Substitute T = 65: 65 = \dfrac{N}{4} + 37.
Subtract 37 from both sides: 28 = \dfrac{N}{4}.
Multiply both sides by 4: N = 112.
The cricket would chirp about 112 times per minute.
Check:\dfrac{112}{4} + 37 = 28 + 37 = 65 ✓
Tip: Decide which letter the given number belongs to before you substitute. Here 65 is a temperature, so it replaces T, not N. Then undo the operations in reverse order: the formula divides by 4 and then adds 37, so you subtract 37 first and multiply by 4 last.
Question 17 of 36
A jar holds 64 coins, all dimes and quarters. The coins are worth $10.90 in total. How many quarters are in the jar?
Hint
If d is the number of dimes, the number of quarters is 64 - d. A dime is worth $0.10 and a quarter $0.25.
Tip: Divide the amount lost (18{,}400 - 8{,}800 = 9{,}600) by the loss per year, not the amount that is left.
Question 20 of 36
A community center spends \tfrac{2}{5} of its yearly budget on staff and \tfrac{1}{4} on the building. The remaining $42,000 is spent on programs. What is the center's total yearly budget?
Hint
First find what fraction of the budget is left for programs. That fraction of the budget equals $42,000.
Step-by-step solution
Let B = the total budget. Fraction used: \dfrac{2}{5} + \dfrac{1}{4} = \dfrac{8}{20} + \dfrac{5}{20} = \dfrac{13}{20}.
Tip: The dollar amount that is "left" matches the fraction that is left, not the fractions that were spent.
Question 21 of 36
No calculator
Luis has $250 in savings. He adds $35 to his savings each week. Which equation can be used to find w, the number of weeks until he has $600 saved?
Hint
Start with what he has now. What happens to that amount each week?
Step-by-step solution
He starts with $250.
Each week he adds $35, so after w weeks he has added 35w dollars.
Total savings after w weeks: 250 + 35w.
He wants the total to be $600: 250 + 35w = 600.
The equation is 250 + 35w = 600.
Check: solving it gives 35w = 350, so w = 10 weeks. After 10 weeks: 250 + 35(10) = 250 + 350 = 600 ✓
Tip: The amount that repeats each week is multiplied by the variable. The one-time starting amount is added on its own.
Question 22 of 36
No calculatorDrop-down
A hardware store rents a carpet cleaner for $45 per day plus a one-time $30 cleaning fee. Kim's total bill was $210. Let d be the number of days she rented the machine.
Select the numbers that complete the equation for Kim's bill.
d + =
Choose an answer from each menu.
Hint
Which amount is charged once for every day? Which amount is charged only one time? Which amount is the total?
Step-by-step solution
The $45 is charged each day, so it is multiplied by d: 45d.
The $30 cleaning fee is charged once, so it is added by itself: +30.
The total bill is $210, so the equation is 45d + 30 = 210.
The equation is 45d + 30 = 210.
Check: solve it. 45d = 180, so d = 4 days. Four days cost 4 \times 45 = \$180, plus the $30 fee, makes $210 ✓
Tip: In a model of the form (\text{rate})\cdot(\text{variable}) + (\text{one-time amount}) = \text{total}, the clue word "per" (per day, per mile, per hour) tells you which number goes with the variable.
Question 23 of 36
Ana earns $18 per hour for the first 40 hours she works in a week. For each hour over 40, she earns time and a half (1.5 times her regular rate). Last week she earned $909. How many hours did she work in total last week?
Hint
First find her pay for 40 regular hours and her overtime rate. Let h be the number of overtime hours.
Step-by-step solution
Regular pay for 40 hours: 40 \times 18 = \$720.
Overtime rate: 1.5 \times 18 = \$27 per hour.
Let h = overtime hours. Total pay: 720 + 27h = 909.
Subtract 720: 27h = 189.
Divide by 27: h = 7 overtime hours.
Total hours = 40 + 7 = 47.
She worked 47 hours in total.
Check:40(18) + 7(27) = 720 + 189 = \$909 ✓
Tip: Multi-step problems often have a "trap" answer that is a middle step (7 overtime hours). Re-read the question — it asks for total hours.
Question 24 of 36
Drag and drop
A tank holds 50 gallons of water. It drains at a steady rate of 2.5 gallons per minute. Drag the correct number of minutes into each box. Two numbers are not used.
The tank holds 20 gallons after minutes.
The tank is empty after minutes.
Tap a tile, then tap a box to place it.
Hint
Water left = 50 - 2.5t. Set this equal to 20, then to 0.
Step-by-step solution
Let t = minutes. The water left in the tank is 50 - 2.5t.
When 20 gallons are left:
50 - 2.5t = 20.
Subtract 50: -2.5t = -30.
Divide by -2.5: t = 12 minutes.
When the tank is empty:
50 - 2.5t = 0.
Add 2.5t: 50 = 2.5t.
Divide by 2.5: t = 20 minutes.
Answer: 12 minutes for 20 gallons; 20 minutes to empty.
Tip: "Holds 20 gallons" means 20 gallons are left, so 30 gallons have drained. Dividing 20 by 2.5 (= 8) finds how long it takes to drain 20 gallons — a different question.
Question 25 of 36
No calculatorSelect all
A phone repair shop charges a $25 diagnostic fee plus $40 per hour of repair work. A customer's bill was $125. Let h be the number of hours of repair work. Select all the equations that correctly model this situation.
Select all that apply.
Hint
Write the basic model first. Then check whether each choice is the same equation rearranged correctly.
Step-by-step solution
Basic model: fee + rate × hours = total, so 25 + 40h = 125. A is correct.
Subtract 25 from both sides of A: 40h = 125 - 25. This is an equivalent equation. B is correct.
C: 40(h + 25) = 125 multiplies the fee by 40, as if it were 25 extra hours. Wrong.
D: Start from 25 + 40h = 125 and subtract 40h from both sides: 25 = 125 - 40h, which is the same as 125 - 40h = 25. D is correct.
E: 25h + 40 = 125 swaps the rate and the fee. Wrong.
The correct choices are A, B, and D.
Check: all three give h = 2.5. A: 25 + 40(2.5) = 125 ✓. B: 40(2.5) = 100 = 125 - 25 ✓. D: 125 - 100 = 25 ✓. C gives h = -21.875 and E gives h = 3.4, so they are different equations.
Tip: Equations that are rearrangements of the correct model (same solution) also model the situation. Test a choice by solving it or by plugging in the true answer.
Question 26 of 36
Maya has $520 and spends $15 of it each week. Theo has $160 and saves $25 more each week. After how many weeks will Maya and Theo have the same amount of money?
Hint
Maya's amount goes down and Theo's goes up. Write an expression for each after w weeks and set them equal.
Tip: When one amount falls and the other rises, the gap closes by the sum of the two rates each week (15 + 25 = 40). The starting gap is 520 - 160 = 360, and 360 \div 40 = 9.
Question 27 of 36
Fill in
Rosa is 4 times as old as her nephew. In 6 years, Rosa will be 2.5 times as old as her nephew.
How old is Rosa now?
years old
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Let n = the nephew's age now. Then Rosa is 4n. In 6 years, both of them are 6 years older.
Step-by-step solution
Let n = nephew's age now. Rosa's age now = 4n.
In 6 years: nephew n + 6, Rosa 4n + 6.
Rosa will be 2.5 times as old: 4n + 6 = 2.5(n + 6).
Distribute: 4n + 6 = 2.5n + 15.
Subtract 2.5n: 1.5n + 6 = 15.
Subtract 6: 1.5n = 9, so n = 6.
Rosa now: 4n = 4(6) = 24.
Rosa is 24 years old now.
Check: now 24 and 6 (24 = 4 \times 6 ✓). In 6 years: 30 and 12, and 30 = 2.5 \times 12 ✓
Tip: In age problems, add the years to every person. Also answer for the right person: here n = 6 is the nephew, but the question asks about Rosa.
Question 28 of 36
Fill in
An isosceles triangle has two equal sides that are each (3x - 2) centimeters long. The third side (the base) is (x + 5) centimeters long. The perimeter of the triangle is 64 centimeters.
How long is each of the two equal sides?
centimeters
Type your answer in the box. Fractions like 3/4 are fine.
Hint
The perimeter is the sum of all three sides, and two of them are 3x - 2.
Step-by-step solution
Perimeter = side + side + base: (3x - 2) + (3x - 2) + (x + 5) = 64.
Combine like terms: 3x + 3x + x = 7x and -2 - 2 + 5 = 1. So 7x + 1 = 64.
Subtract 1: 7x = 63.
Divide by 7: x = 9.
Each equal side: 3x - 2 = 3(9) - 2 = 27 - 2 = 25 cm. (The base is 9 + 5 = 14 cm.)
Each equal side is 25 centimeters.
Check:25 + 25 + 14 = 64 ✓
Tip: Count every side in a perimeter. An isosceles triangle has two equal sides, so the expression 3x - 2 appears twice. Then substitute x back to get the length the question asks for.
Question 29 of 36
Fill in
After a 15% raise, Dana now earns $20.70 per hour. What was her hourly pay before the raise?
$ per hour
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Her new pay is her old pay plus 15% of her old pay. Write that as one number times the old pay.
Step-by-step solution
Let w = old hourly pay. The raise is 0.15w, so the new pay is w + 0.15w = 1.15w.
Equation: 1.15w = 20.70.
Divide by 1.15: w = \dfrac{20.70}{1.15} = 18.
Her pay before the raise was $18.00 per hour.
Check: 15% of $18 is 0.15 \times 18 = \$2.70, and 18 + 2.70 = \$20.70 ✓
Tip: Do not take 15% off the new amount: 20.70 - 0.15(20.70) \approx 17.60 is wrong, because the raise was 15% of the old pay. Divide by 1.15 instead.
Question 30 of 36
Carla drove from her home to a lake at an average speed of 60 miles per hour. She drove home on the same road at 40 miles per hour. The round trip took 5 hours of driving. How far is the lake from her home?
Hint
Let d = the one-way distance. Time = distance ÷ speed for each part. The two times add to 5 hours.
Step-by-step solution
Let d = one-way distance in miles. Time there = \dfrac{d}{60}; time back = \dfrac{d}{40}.
Total time: \dfrac{d}{60} + \dfrac{d}{40} = 5.
Multiply every term by the LCD, 120: 2d + 3d = 600.
Tip: You cannot simply average the two speeds (50 mph), because she spends more time at the slower speed. Write a time expression for each part instead.
Question 31 of 36
Fill in
A fitness trainer uses the formula
R = 0.7(220 - a)
to find a client's target heart rate R (in beats per minute) during exercise, where a is the client's age in years. A client's target heart rate is 133 beats per minute. How old is the client?
years old
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Put 133 in for R. Undo the multiplication by 0.7 first, then solve for a.
Step-by-step solution
Substitute R = 133: 133 = 0.7(220 - a).
Divide both sides by 0.7: \dfrac{133}{0.7} = 220 - a, so 190 = 220 - a.
Subtract 220 from both sides: -30 = -a.
Multiply by -1: a = 30.
The client is 30 years old.
Check:0.7(220 - 30) = 0.7(190) = 133 ✓
Tip: Dividing by 0.7 first avoids distributing decimals. Watch the sign at the end: 190 = 220 - a means a = 220 - 190, which is positive.
Question 32 of 36
Drag and drop
A new candle is 12 inches tall. It burns down at a steady rate of 0.75 inch per hour. Drag the correct number of hours into each box. Three numbers are not used.
The candle is 7.5 inches tall after hours.
The candle burns down completely after hours.
Tap a tile, then tap a box to place it.
Hint
Height after h hours = 12 - 0.75h. Set that equal to each height in the question.
Tip: The unused tiles come from common errors: 10 divides the height that is left (7.5) by the rate, 26 adds the heights instead of subtracting, and 9 multiplies 12 by 0.75 instead of dividing.
Question 33 of 36
Jordan spent \tfrac{1}{3} of his paycheck on rent. He then spent $150 on groceries. After that, he had \tfrac{1}{4} of his paycheck left. How much was his paycheck?
Hint
Let p = the paycheck. Rent + groceries + money left must add up to the whole paycheck p.
Step-by-step solution
Let p = paycheck. Rent = \tfrac{1}{3}p, groceries = 150, left over = \tfrac{1}{4}p.
All the parts add up to the whole: \tfrac{1}{3}p + 150 + \tfrac{1}{4}p = p.
Multiply every term by the LCD, 12: 4p + 1800 + 3p = 12p.
Tip: In "fraction of the whole" problems, write an equation where all the parts add up to the whole amount. Then clear the fractions with the LCD.
Question 34 of 36
Fill in
A coffee shop mixes beans that cost $9 per pound with beans that cost $14 per pound. It wants 50 pounds of a blend that is worth $11 per pound.
How many pounds of the $9 beans should it use?
pounds
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Let x = pounds of $9 beans, so 50 - x pounds are $14 beans. The total value of the beans must equal 50 pounds × $11.
Step-by-step solution
Let x = pounds of $9 beans. Then 50 - x = pounds of $14 beans.
Value of the blend: 50 \times 11 = \$550.
Value equation: 9x + 14(50 - x) = 550.
Distribute: 9x + 700 - 14x = 550.
Combine like terms: -5x + 700 = 550.
Subtract 700: -5x = -150.
Divide by -5: x = 30.
The shop should use 30 pounds of the $9 beans (and 50 - 30 = 20 pounds of the $14 beans).
Check:30(9) + 20(14) = 270 + 280 = \$550, and 550 \div 50 = \$11 per pound ✓
Tip: The blend price ($11) is closer to $9 than to $14, so the blend needs more of the $9 beans. That quick estimate tells you the answer must be more than 25 pounds.
Question 35 of 36
An electric company bills customers each month as follows:
Part of the bill
Charge
Monthly service charge
$12.00
First 500 kWh
$0.11 per kWh
Each kWh over 500
$0.15 per kWh
A customer's bill for one month was $106.00. How many kilowatt-hours (kWh) did the customer use?
Hint
First find the cost of the service charge plus a full 500 kWh. The rest of the bill pays for kWh over 500.
Step-by-step solution
Cost of the service charge and the first 500 kWh: 12 + 0.11(500) = 12 + 55 = \$67.
The bill is more than $67, so the customer used more than 500 kWh. Let k = total kWh. The extra kWh are k - 500.
Tip: With tiers, fill up the first tier completely, then let the remaining money buy units at the higher rate. Add the tier amounts back together at the end.
Question 36 of 36
A hiker walked \tfrac{1}{3} of a trail in the morning. After lunch, she walked \tfrac{1}{2} of the remaining distance. She still has 4.5 miles left to walk. How long is the whole trail?
Hint
Let L = trail length. After the morning, \tfrac{2}{3}L remains. After lunch she walks half of that, not half of the trail.
Step-by-step solution
Let L = the length of the trail. Morning: \tfrac{1}{3}L, so \tfrac{2}{3}L remains.
After lunch she walks \tfrac{1}{2} of \tfrac{2}{3}L, which is \tfrac{1}{3}L.
