Tip: Consecutive integers: n, n + 1. Consecutive even or odd integers: n, n + 2. "Product" = multiply; "sum" = add.
Question 3 of 36
Fill in
A square bedroom has an area of 144 square feet. Write an equation for the side length s and solve it.
What is the side length of the room, in feet?
feet
Type your answer in the box. Fractions like 3/4 are fine.
Hint
The area of a square is the side length times itself.
Step-by-step solution
The area of a square is s \times s = s^2.
Equation: s^2 = 144
Take the square root of both sides: s = \pm\sqrt{144} = \pm 12.
A length can't be negative, so reject -12. The side length is 12 feet.
Check:12 \times 12 = 144 ✓
Tip: Square-root equations give a \pm answer, but in real-world measurements you keep only the positive value. Dividing by 4 (144 \div 4 = 36) gives the side from a perimeter, not an area.
Question 4 of 36
No calculator
A triangular sail has a base that is 4 feet longer than its height, h. The area of the sail is 30 square feet.
Which equation can be used to find h?
Hint
The area of a triangle is \tfrac{1}{2} \times \text{base} \times \text{height}. Write the base in terms of h first.
Step-by-step solution
Let the height be h feet. The base is 4 feet longer, so the base is h + 4 feet.
The triangle area formula (on the GED formula sheet) is A = \tfrac{1}{2}bh.
Substitute the base h + 4, the height h and the area 30:
\frac{1}{2}h(h + 4) = 30
The equation is \tfrac{1}{2}h(h + 4) = 30.
Check: Solve it: multiply by 2 to get h^2 + 4h = 60, so h^2 + 4h - 60 = (h + 10)(h - 6) = 0 and h = 6. Then the base is 10, and \tfrac{1}{2}(10)(6) = 30 ✓
Tip: Triangles always need the \tfrac{1}{2}. Without it you are finding the area of a rectangle with the same base and height — twice as big.
Question 5 of 36
No calculator
The product of two consecutive even integers is 168. Let n be the smaller integer.
Which equation can be used to find n?
Hint
Even integers like 4, 6, 8 are how far apart? Use that to write the larger integer in terms of n.
Step-by-step solution
Consecutive even integers go up by 2 (for example 12, 14, 16). If the smaller one is n, the next even integer is n + 2.
"Product" means multiply:
n(n + 2) = 168
The equation is n(n + 2) = 168.
Check: Solve: n^2 + 2n - 168 = 0 factors as (n + 14)(n - 12) = 0. With n = 12: 12 \times 14 = 168 ✓, and both 12 and 14 are even ✓
Tip: Consecutive integers: n, n + 1. Consecutive even or consecutive odd integers: n, n + 2 — both kinds are 2 apart.
Question 6 of 36
No calculatorFill in
A rectangular rug is twice as long as it is wide. The area of the rug is 72 square feet.
What is the width of the rug, in feet?
feet
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Call the width w. Write the length in terms of w, then multiply to get the area.
Step-by-step solution
Let w = the width in feet. The rug is twice as long as it is wide, so the length is 2w.
Area = length × width:
2w \cdot w = 72 \;\Rightarrow\; 2w^2 = 72
Divide both sides by 2: w^2 = 36.
Take the square root: w = \pm 6. A width cannot be negative, so w = 6.
The width is 6 feet (and the length is 12 feet).
Check:12 \times 6 = 72 square feet ✓, and 12 is twice 6 ✓
Tip: Read what the question asks for. Here it is the width; the length (12 ft) would be a wrong answer even though it comes from the same work.
Question 7 of 36
No calculator
The height h, in feet, of an object thrown upward is h = -16t^2 + v_0 t + h_0, where t is the time in seconds, v_0 is the starting upward speed in feet per second and h_0 is the starting height in feet.
A lifeguard tosses a rescue ring upward from a tower 20 feet above the water with a starting speed of 24 feet per second. Which equation can be used to find when the ring hits the water?
Hint
Which number is the starting height and which is the speed? What is the height when the ring hits the water?
Step-by-step solution
Match the numbers to the formula:
starting speed v_0 = 24 ft/s (it multiplies t)
starting height h_0 = 20 ft (the constant)
So the height is h = -16t^2 + 24t + 20.
The water is at height 0, so the ring hits the water when h = 0:
-16t^2 + 24t + 20 = 0
The equation is -16t^2 + 24t + 20 = 0.
Check: At t = 0 the equation gives h = 20 — the ring starts on the 20-ft tower ✓. Solving (4t^2 - 6t - 5 = 0) gives t \approx 2.1 seconds, a reasonable time.
Tip: Label each number before substituting: speed goes with t, starting height stands alone, and "hits the ground/water" means h = 0.
Question 8 of 36
No calculator
The length of a rectangular garden is 1 foot less than twice its width, w. The area of the garden is 105 square feet.
Which equation, written in standard form, can be used to find w?
Hint
First write the length in terms of w. Then write length × width = 105, multiply out, and move everything to one side.
Step-by-step solution
Length is "1 less than twice the width": 2w - 1.
Area: w(2w - 1) = 105
Distribute: 2w^2 - w = 105.
Subtract 105 from both sides: 2w^2 - w - 105 = 0
The answer is 2w^2 - w - 105 = 0.
Check: Quadratic formula: w = \dfrac{1 \pm \sqrt{1 + 840}}{4} = \dfrac{1 \pm 29}{4}, so w = 7.5 (reject -7). Length = 2(7.5) - 1 = 14. Area = 7.5 \times 14 = 105 ✓
Tip: When you distribute, multiply the outside term by every term inside: w(2w - 1) = 2w^2 - w.
Question 9 of 36
Fill in
The product of two consecutive positive odd integers is 143.
What is the smaller integer?
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Odd numbers are 2 apart. If the smaller one is n, what is the next odd number?
Step-by-step solution
Let n = the smaller odd integer. The next odd integer is n + 2.
Equation: n(n + 2) = 143
Standard form: n^2 + 2n - 143 = 0.
Find two numbers that multiply to -143 and add to 2: 13 and -11.
Factor: (n + 13)(n - 11) = 0, so n = 11 or n = -13.
The integers are positive, so n = 11. The smaller integer is 11 (the pair is 11 and 13).
Check:11 \times 13 = 143 ✓; both are odd and 2 apart ✓
Tip: A quick estimate helps: \sqrt{143} \approx 12, so the two odd numbers sit on either side of 12 — 11 and 13.
Question 10 of 36
No calculator
A 12-inch by 9-inch photo is placed in a frame that has the same width, x inches, on every side. The total area of the photo and frame together is 208 square inches.
Which equation can be used to find x?
Hint
The frame adds x to the left andx to the right. How long is the whole outside edge?
Step-by-step solution
The frame adds x on both ends of each side, so each dimension grows by 2x.
Outer length: 12 + 2x. Outer width: 9 + 2x.
Total area = outer length × outer width: (12 + 2x)(9 + 2x) = 208
Tip: Look for the operation words: "product" and "area" → multiply; "sum" and "perimeter" → add.
Question 12 of 36
No calculator
The height h, in feet, of an object thrown straight up is given by h = -16t^2 + v_0 t + h_0, where t is the time in seconds, v_0 is the starting upward speed in feet per second, and h_0 is the starting height in feet.
Marcus throws a ball upward from a height of 5 feet with a starting speed of 48 feet per second. Which equation can be used to find when the ball is 37 feet above the ground?
Hint
Identify v_0 and h_0 from the story. Which variable stands for the height you want?
Step-by-step solution
From the story: v_0 = 48 ft/s and h_0 = 5 ft.
The height model is h = -16t^2 + 48t + 5.
We want the height to be 37 ft, so set h = 37: -16t^2 + 48t + 5 = 37
The answer is -16t^2 + 48t + 5 = 37.
Check: Solve: -16t^2 + 48t - 32 = 0; divide by -16: t^2 - 3t + 2 = 0 \Rightarrow (t - 1)(t - 2) = 0, so t = 1 s (on the way up) or t = 2 s (on the way down). At t = 2: -64 + 96 + 5 = 37 ✓
Tip: The target height goes where h is — not in place of h_0. Set the expression equal to the height you are asked about.
Question 13 of 36
Fill in
A model rocket is launched straight up from the ground. Its height h, in feet, after t seconds is
h = -16t^2 + 80t
After how many seconds does the rocket land back on the ground?
seconds
Type your answer in the box. Fractions like 3/4 are fine.
Hint
On the ground, the height is 0. Set up that equation and look for a common factor.
Step-by-step solution
On the ground, h = 0: -16t^2 + 80t = 0
Factor out the common factor -16t: -16t(t - 5) = 0
Zero product property: -16t = 0 \Rightarrow t = 0, or t - 5 = 0 \Rightarrow t = 5.
t = 0 is the launch moment (the rocket starts on the ground). It lands at t = 5.
Tip: When there is no constant term, factor out the GCF. One solution is t = 0 (the start); the answer is the other one.
Question 14 of 36
No calculator
A rectangular sign is 5 feet longer than it is wide. Its area is 84 square feet. Rosa writes the equation w(w + 5) = 84 and finds the solutions w = 7 and w = -12.
Which statement about the width of the sign is correct?
Hint
Both numbers make the equation true. Which one can be the width of a real sign?
Step-by-step solution
Check both solutions in the equation:
w = 7: 7(12) = 84 ✓
w = -12: (-12)(-7) = 84 ✓
Both solve the equation, but the problem is about a real sign. A width is a length, so it cannot be negative.
Reject w = -12. The width is 7 feet (and the length is 7 + 5 = 12 feet).
Check: A 7-ft by 12-ft sign has area 7 \times 12 = 84 sq ft ✓
Tip: After solving a word problem, always ask "Does this answer make sense?" Lengths, times, ages and counts cannot be negative.
Question 15 of 36
Fill in
When a book is open, the two facing page numbers are consecutive integers. Ana notices that the two facing page numbers multiply to 210.
What is the larger page number?
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Let n be the smaller page number. Write and solve n(n + 1) = 210. Then read the question again.
Step-by-step solution
Let n = the smaller integer. The next integer is n + 1.
Product is 210:
n(n + 1) = 210 \;\Rightarrow\; n^2 + n - 210 = 0
Factor: we need two numbers with product -210 and sum 1: 15 and -14.
(n + 15)(n - 14) = 0 \;\Rightarrow\; n = -15 \text{ or } n = 14
Page numbers are positive, so n = 14 and the larger page number is n + 1 =15.
Check:14 \times 15 = 210 ✓
Tip: Shortcut: \sqrt{210} \approx 14.5, so the two consecutive integers sit on either side — 14 and 15. Then make sure you give the one the question asks for.
Question 16 of 36
No calculatorFill in
A soccer ball is kicked from the ground. Its height h, in feet, after t seconds is
h = -16t^2 + 48t
After how many seconds is the ball 32 feet high for the first time?
seconds
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Set the height equal to 32 and get 0 on one side. Dividing every term by the same number can make factoring easier.
Step-by-step solution
Set h = 32:
-16t^2 + 48t = 32
Subtract 32 to get standard form:
-16t^2 + 48t - 32 = 0
Divide every term by -16:
t^2 - 3t + 2 = 0
Factor: (t - 1)(t - 2) = 0, so t = 1 or t = 2.
The ball is 32 ft high on the way up at 1 second and on the way down at 2 seconds. The first time is 1 second.
Tip: A thrown object usually passes each height twice. "First time" means the smaller positive time.
Question 17 of 36
No calculator
The right triangle shows a loading ramp. The rise is x feet, the horizontal run is 7 feet more than the rise, and the sloped surface is 13 feet long.
Which equation can be used to find x?
Hint
The Pythagorean theorem a^2 + b^2 = c^2 is on the formula sheet. Which side is c?
Step-by-step solution
In a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse — the side across from the right angle.
Here the legs are x and x + 7, and the hypotenuse (the sloped surface) is 13.
Substitute:
x^2 + (x + 7)^2 = 13^2
The equation is x^2 + (x + 7)^2 = 13^2.
Check: Solve: x^2 + x^2 + 14x + 49 = 169, so 2x^2 + 14x - 120 = 0, or x^2 + 7x - 60 = (x + 12)(x - 5) = 0. Then x = 5: legs 5 and 12, and 25 + 144 = 169 = 13^2 ✓
Tip: Square every side, including the hypotenuse, and remember (x + 7)^2 = x^2 + 14x + 49, not x^2 + 49.
Question 18 of 36
No calculator
The square of a number is 24 more than 5 times the number.
What are all the possible values of the number?
Hint
"24 more than 5 times the number" means you start with 5x and add 24. Nothing says the number must be positive.
Step-by-step solution
Let x be the number. Translate: "the square of a number" is x^2; "24 more than 5 times the number" is 5x + 24.
x^2 = 5x + 24
Standard form: x^2 - 5x - 24 = 0.
Factor: product -24, sum -5 → -8 and 3:
(x - 8)(x + 3) = 0
So x = 8 or x = -3. The problem does not say "positive," so both work: 8 or -3.
Check:8^2 = 64 and 5(8) + 24 = 64 ✓. (-3)^2 = 9 and 5(-3) + 24 = 9 ✓
Tip: Reject a negative answer only when the situation makes it impossible (a length, a time, a count). A plain "number" can be negative.
Question 19 of 36
No calculator
A bakery sells 200 loaves of bread a day at $4 each. The owner estimates that for every $0.50 increase in price, she will sell 10 fewer loaves.
Let x be the number of $0.50 increases. Which expression gives the daily revenue, in dollars?
Hint
Revenue = (price per loaf) × (number of loaves). Write each one in terms of x.
Step-by-step solution
Price: each increase adds $0.50, so after x increases the price is 4 + 0.5x dollars.
Loaves sold: each increase loses 10 loaves, so she sells 200 - 10x loaves.
Revenue = price × number sold:
R = (4 + 0.5x)(200 - 10x)
The expression is (4 + 0.5x)(200 - 10x).
Check: Try x = 2: price 4 + 1 = \$5, loaves 200 - 20 = 180, revenue 5 \times 180 = \$900. The expression gives (5)(180) = 900 ✓. At x = 0 it gives 4 \times 200 = \$800, today's revenue ✓
Tip: Test your model with x = 0 (it should give today's numbers) and x = 1 (one step of change).
Question 20 of 36
A rectangular vegetable garden is 12 feet by 9 feet. A gravel path of the same width, x feet, will surround the garden on all sides. The garden and path together will cover 180 square feet.
How wide is the path?
Hint
The path adds x on both ends of each side. Write the new length and width, multiply, and set the result equal to 180.
Step-by-step solution
The path adds x on each end, so the outer length is 12 + 2x and the outer width is 9 + 2x.
Factor (product -1200, sum -10 → -40 and 30): (w - 40)(w + 30) = 0, so w = 40 or w = -30.
A width cannot be negative, so the width is 40 inches (height 30 inches).
Check:40^2 + 30^2 = 1600 + 900 = 2500 = 50^2 ✓
Tip: TV and monitor sizes are measured on the diagonal, so screen problems are right-triangle problems in disguise.
Question 23 of 36
The sum of a positive number and its square is 110. What is the number?
Hint
Write "a number plus its square equals 110," move everything to one side, and factor.
Step-by-step solution
Let x = the number. "The sum of a number and its square": x + x^2 = 110
Standard form: x^2 + x - 110 = 0.
Find two numbers that multiply to -110 and add to 1: 11 and -10.
Factor: (x + 11)(x - 10) = 0, so x = -11 or x = 10.
The number is positive, so the answer is 10.
Check:10 + 10^2 = 10 + 100 = 110 ✓
Tip: Read every condition. -11 also solves the equation (-11 + 121 = 110), but the problem says the number is positive.
Question 24 of 36
Fill in
A rectangular pool is 30 feet by 20 feet. A concrete walkway of the same width, x feet, surrounds the pool on all sides. The area of the walkway alone is 336 square feet.
How wide is the walkway, in feet?
feet
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Walkway area = (area of the big outer rectangle) − (area of the pool). Each outer dimension is the pool dimension plus 2x.
Step-by-step solution
Outer rectangle: (30 + 2x) by (20 + 2x). Pool area: 30 \times 20 = 600.
Walkway area = outer area − pool area: (30 + 2x)(20 + 2x) - 600 = 336
Tip: When only the border's area is given, subtract the inner area. Forgetting this (setting the outer area equal to 336) gives an impossible equation, since the pool alone is already 600 ft².
Question 25 of 36
No calculator
A ball is thrown upward from the roof of a garage. Its height h, in feet, after t seconds is
h = -16t^2 + 32t + 48
After how many seconds does the ball hit the ground?
Hint
The ground is height 0. Divide every term by -16 before factoring.
Step-by-step solution
The ball hits the ground when h = 0:
-16t^2 + 32t + 48 = 0
Divide every term by -16:
t^2 - 2t - 3 = 0
Factor (product -3, sum -2 → -3 and 1):
(t - 3)(t + 1) = 0 \;\Rightarrow\; t = 3 \text{ or } t = -1
Time after the throw cannot be negative, so the ball hits the ground after 3 seconds.
Check:-16(9) + 32(3) + 48 = -144 + 96 + 48 = 0 ✓
Tip: Dividing by the common factor (-16) first turns a messy equation into an easy one to factor.
Question 26 of 36
No calculatorSelect all
A raised garden bed is 3 feet longer than it is wide. Its area is 40 square feet. Kwame models this with w(w + 3) = 40, where w is the width in feet.
Select all the statements that are true.
Select all that apply.
Hint
Solve the equation first. Then decide which solution fits a real garden bed, and find both dimensions.
Step-by-step solution
Standard form: w^2 + 3w - 40 = 0.
Factor (product -40, sum 3 → 8 and -5): (w + 8)(w - 5) = 0, so w = -8 or w = 5.
Judge each statement:
"The equation has solutions 5 and -8." True ✓
"The width is 5 feet." True ✓ — a width cannot be negative, so w = 5.
"The length is 8 feet." True ✓ — length = w + 3 = 8.
"The width could be -8 feet." False — negative lengths are impossible.
"The length is 5 feet." False — 5 ft is the width.
True statements: the solutions are 5 and -8; the width is 5 ft; the length is 8 ft.
Check:5 \times 8 = 40 ✓ and 8 - 5 = 3 ✓
Tip: Separate "solutions of the equation" (both roots) from "answers to the problem" (only those that make sense).
Question 27 of 36
No calculatorDrag and drop
Drag the equation that models each situation into the box below it. Let n be the smaller integer. Not every equation is used.
Two consecutive odd integers have a product of 195.
The squares of two consecutive integers add up to 61.
Two consecutive integers have a product of 240.
Tap a tile, then tap a box to place it.
Hint
Decide first whether the integers are 1 apart or 2 apart. Then decide whether the words describe a product or a sum of squares.
Step-by-step solution
Consecutive odd integers are 2 apart: n and n + 2. Product 195: n(n + 2) = 195.
Consecutive integers are 1 apart: n and n + 1. "The squares add up to 61": n^2 + (n + 1)^2 = 61.
Consecutive integers with product 240: n(n + 1) = 240.
Tip: "Odd" or "even" → step of 2. Plain "consecutive integers" → step of 1. Then read the operation words: "product" (multiply) vs "squares add up to" (square each, then add).
Question 28 of 36
A rectangular parking lot is 20 feet longer than it is wide. Its area is 2,400 square feet.
What is the width of the parking lot?
Hint
Write w(w + 20) = 2400, move everything to one side, and factor. Then read which dimension the question wants.
Step-by-step solution
Let w = width. Length = w + 20. Area:
w(w + 20) = 2400 \;\Rightarrow\; w^2 + 20w - 2400 = 0
Factor: two numbers with product -2400 and sum 20 → 60 and -40:
(w + 60)(w - 40) = 0
So w = -60 or w = 40. A width cannot be negative, so w = 40.
The width is 40 feet (the length is 60 feet).
Check:40 \times 60 = 2{,}400 ✓ and 60 - 40 = 20 ✓
Tip: Don't take \sqrt{2400} — that only works for a square. A rectangle with different sides needs the full quadratic.
Question 29 of 36
Fill in
A bike shop rents 40 bikes a day at $25 each. For every $5 increase in the daily price, it rents 4 fewer bikes.
The shop wants to bring in $1,120 a day. What is the lowest daily price, in dollars, that will do this?
$
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Let x be the number of $5 increases. Write (price)(bikes rented) = 1120, solve for x, then turn x into a price.
Step-by-step solution
Let x = number of $5 increases. Price = 25 + 5x; bikes rented = 40 - 4x.
Factor (product -120, sum 7 → 15 and -8): (w + 15)(w - 8) = 0, so w = 8 (reject -15).
The width is 8 yards (length 15 yards).
Check:8^2 + 15^2 = 64 + 225 = 289 = 17^2 ✓
Tip: Know the common Pythagorean triples — 3-4-5, 5-12-13, 8-15-17, 7-24-25. They let you check answers fast.
Question 31 of 36
No calculator
The height h, in feet, of an object launched upward is h = -16t^2 + v_0 t + h_0, where t is time in seconds, v_0 is the starting upward speed in feet per second and h_0 is the starting height in feet.
A firework is launched from a platform 8 feet high with a starting speed of 120 feet per second. Which equation, in standard form, can be solved to find when the firework is 200 feet high?
Hint
Substitute v_0, h_0 and h = 200. Then move 200 to the left side. Multiplying every term of an equation by -1 gives an equivalent equation.
Step-by-step solution
Substitute v_0 = 120, h_0 = 8 and h = 200:
-16t^2 + 120t + 8 = 200
Subtract 200 from both sides:
-16t^2 + 120t - 192 = 0
Multiply every term by -1 (this does not change the solutions):
16t^2 - 120t + 192 = 0
The answer is 16t^2 - 120t + 192 = 0.
Check: Divide by 8: 2t^2 - 15t + 24 = 0. The discriminant is 225 - 192 = 33 > 0, so there are two positive times (t \approx 2.3 s going up and t \approx 5.2 s coming down) — sensible for a firework ✓
Tip: Watch for answer choices that are your equation multiplied by -1 or divided by a common factor. When you multiply by -1, change the sign of every term.
Question 32 of 36
No calculatorFill in
When a positive number is multiplied by a number that is 3 less than it, the result is 108.
What is the number?
Type your answer in the box. Fractions like 3/4 are fine.
Hint
If the number is x, the other number is x - 3. Multiply, set equal to 108 and factor.
Step-by-step solution
Let x = the number. "3 less than it" is x - 3.
Their product is 108:
x(x - 3) = 108 \;\Rightarrow\; x^2 - 3x - 108 = 0
Factor: product -108, sum -3 → -12 and 9:
(x - 12)(x + 9) = 0
So x = 12 or x = -9. The number is positive, so the number is 12.
Check:12 \times (12 - 3) = 12 \times 9 = 108 ✓
Tip: "3 less than x" is x - 3 (not 3 - x). The word "positive" in the problem tells you which solution to keep.
Question 33 of 36
No calculator
A ball is thrown from a balcony. Its height in feet after t seconds is h = -16t^2 + 64t + 80. To find when it hits the ground, Maria solves -16t^2 + 64t + 80 = 0 and gets t = 5 and t = -1.
Which statement is correct?
Hint
Both values solve the equation. What does a negative time mean in this situation?
The model starts at t = 0, the moment of the throw. A negative time would be before the ball was thrown, so it has no meaning here.
Reject t = -1. The ball hits the ground after 5 seconds; t = -1 is rejected because it is before the throw.
Check: At t = 0 the ball is at 80 ft (the balcony), at t = 2 it is at -64 + 128 + 80 = 144 ft (going up), and at t = 5 it reaches 0 ft ✓
Tip: The time in the air is the positive root itself, measured from t = 0. Don't add or subtract the two roots.
Question 34 of 36
A community theater charges $12 per ticket and sells 300 tickets per show. A survey shows that for every $1 increase in the ticket price, the theater will sell 15 fewer tickets.
Let x be the number of $1 increases. Which equation can be used to find the value(s) of x that would bring in $3,825 per show?
Hint
Revenue = (price per ticket) × (number of tickets). Write each one in terms of x.
Step-by-step solution
Price per ticket after x increases: 12 + x dollars.
Tickets sold: each increase loses 15 tickets, so 300 - 15x.
Factor (product -168, sum 2 → 14 and -12): (n + 14)(n - 12) = 0, so n = 12 or n = -14.
The integers are positive, so n = 12 and the larger integer is 14.
Check:12^2 + 14^2 = 144 + 196 = 340 ✓
Tip:(n + 2)^2 = n^2 + 4n + 4. Writing it as n^2 + 4 is one of the most common algebra mistakes on the test.
Question 36 of 36
Fill in
A rectangular yard is 40 feet by 25 feet. A flower border of the same width, x feet, is planted along the inside edges of the yard. The grass left in the middle has an area of 646 square feet.
How wide is the flower border, in feet?
feet
Type your answer in the box. Fractions like 3/4 are fine.
Hint
The border takes x off both ends of each side, so the grass is (40 - 2x) by (25 - 2x). One solution of the equation will be too big to fit in the yard.
Step-by-step solution
The grass rectangle measures (40 - 2x) by (25 - 2x):
(40 - 2x)(25 - 2x) = 646
