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

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by BTGModeratorVI » Tue Dec 15, 2020 7:00 am

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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: official guide
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Re: The area of a rectangular garden would be increased by 150 square feet

by swerve » Tue Dec 15, 2020 7:28 am
BTGModeratorVI wrote: ↑
Tue Dec 15, 2020 7:00 am
 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: official guide
Let \(x= L\cdot W\)
\(x\) is original area
\(L\) length and \(W\) width

Now as per given info
\(x+150 = (L+7.5)W\)
Or
\(x+150 = (W+5)L\)

Now equating the above equations we get, \(L=\dfrac{3}{2} W\)

Plug this value in any of the above equations.
Put \(x= L\cdot W\)

And form an equation in the form of \(W\).

We will get \(W=20\) and \(L=30\)

So original area \(x=L\cdot W=30\cdot 20=600\)
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Re: The area of a rectangular garden would be increased by 150 square feet

by Brent@GMATPrepNow » Tue Dec 15, 2020 7:36 am
BTGModeratorVI wrote: ↑
Tue Dec 15, 2020 7:00 am
 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: official guide
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

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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