The area of a rectangular garden would be increased by 150 square feet if either the length were increased by 7.5 feet or the width were increased by 5 feet. What is the area of the garden, in square feet?
A. 600
B. 525
C. 375
D. 300
E. 225
Answer; A
Source: GMAT prep
The area of a rectangular garden would be increased by 150
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Ooops!BTGModeratorVI wrote: ↑Mon May 25, 2020 7:36 amThe area of a rectangular garden would be increased by 150 square feet if either the length were increased by 7.5 feet or the width were increased by 5 feet. What is the area of the garden, in square feet?
A. 600
B. 525
C. 375
D. 300
E. 225
Answer; A
Source: GMAT prep
Last edited by Brent@GMATPrepNow on Tue May 26, 2020 5:08 am, edited 1 time in total.
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Brent@GMATPrepNow wrote: ↑Tue May 26, 2020 5:06 amLet L = the ORIGINAL length of the rectangleBTGModeratorVI wrote: ↑Mon May 25, 2020 7:36 amThe area of a rectangular garden would be increased by 150 square feet if either the length were increased by 7.5 feet or the width were increased by 5 feet. What is the area of the garden, in square feet?
A. 600
B. 525
C. 375
D. 300
E. 225
Answer; A
Source: GMAT prep
Let W = the ORIGINAL width of the rectangle
So, LW = the ORIGINAL area of the rectangle
The area of a rectangular garden would be increased by 150 square feet if the length were increased by 7.5 feet
So we have the following "word equation": (area of NEW rectangle) - (area of ORIGINAL rectangle) = 150
NEW length = L + 7.5
In this case, the width remains at W
So, the NEW area = (L + 7.5)(W)
Plug values into the word equation to get: (L + 7.5)(W) - LW = 150
Expand: LW + 7.5W - LW = 150
Simplify: 7.5W = 150
Divide both sides by 7.5 to get: W = 20
The area of a rectangular garden would be increased by 150 square feet if the width were increased by 5 feet
Once again, we have the "word equation": (area of NEW rectangle) - (area of ORIGINAL rectangle) = 150
NEW with = W + 5
In this case, the length remains at L
So, the NEW area = (L)(W + 5)
Plug values into the word equation to get: (L)(W + 5) - LW = 150
Expand: LW + 5L - LW = 150
Simplify: 5L = 150
Divide both sides by 5 to get: L = 30
What is the area of the garden, in square feet?
ORIGINAL area of the rectangle = LW
= (30)(20)
= 600
Answer: A
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Brent
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Solution:BTGModeratorVI wrote: ↑Mon May 25, 2020 7:36 amThe area of a rectangular garden would be increased by 150 square feet if either the length were increased by 7.5 feet or the width were increased by 5 feet. What is the area of the garden, in square feet?
A. 600
B. 525
C. 375
D. 300
E. 225
Answer; A
Let L = the length of the garden and W = the width of the garden. We can create the equations:
(L + 7.5)W = LW + 150
and
L(W + 5) = LW + 150
Solving the first equation, we have:
LW + 7.5W = LW + 150
7.5W = 150
W = 20
Solving the second equation, we have:
LW + 5L = LW + 150
5L = 150
L = 30
Therefore, the area of the garden is 30 x 20 = 600 sq. ft.
Answer: A
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