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# The area of a rectangular garden would be increased by 150 square feet

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The area of a rectangular garden would be increased by 150 square feet [#permalink]
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Bunuel wrote:
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
PS21198

Let L = the ORIGINAL length of the rectangle
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

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 24 May 2020, 08:16.
Last edited by BrentGMATPrepNow on 15 Dec 2020, 08:38, edited 1 time in total.
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Re: The area of a rectangular garden would be increased by 150 square feet [#permalink]
A.

Let length = l feet
Area = lb sq feet

Case I:
A + 150 = (l+7.5)b
lb + 150 = lb + 7.5b
150 = 7.5b
=> b = 20 feet

Case II:
A + 150 = l(b+5)
lb + 150 = lb + 5l
150 = 5l
=> l = 30 feet

Area = l*b = 30 * 20 = 600 sqaure feet
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Re: The area of a rectangular garden would be increased by 150 square feet [#permalink]
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We get 2 equations,
(x+7.5) * y = xy + 150 -- 1
x* ( y +5 ) = xy + 150 -- 2

from eq 1, y = 20.
from eq 2, x = 30.
xy ( area ) = 600.
Option A
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Re: The area of a rectangular garden would be increased by 150 square feet [#permalink]
Bunuel wrote:
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

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.

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Re: The area of a rectangular garden would be increased by 150 square feet [#permalink]
Area of rectangle = $$lw$$

If either the length were increased by 7.5 ft or width were increased by 5 ft = area will be increased by 150

$$l(w+5) = lw + 150$$

$$lw + 5l = lw + 150$$

$$l = 30$$

$$w(l+7.5) = lw + 150$$

$$lw + 7.5w = lw + 150$$

$$w = 20$$

$$lw = 20 * 30 = 600$$

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Re: The area of a rectangular garden would be increased by 150 square feet [#permalink]
Bunuel wrote:
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

PS21198

why is D incorrect? if the length is 10 and 30... the answer would still work
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Re: The area of a rectangular garden would be increased by 150 square feet [#permalink]
Bunuel wrote:
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

PS21198

why is D incorrect? if the length is 10 and 30... the answer would still work
Re: The area of a rectangular garden would be increased by 150 square feet [#permalink]
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