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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
PS21198
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A. 600
B. 525
C. 375
D. 300
E. 225
PS21198
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Bunuel
Area = l*b
New Area = 150+l*b = (l+7.5)*b
i.e b = 20
New Area = 150+l*b = (l)*(b+5)
i.e l = 30
Area = l*b = 30*20 = 600
Answer: Option A
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General Discussion
Let X= L 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 above equation we get, L=3/2 W
Plug this value in any of above equation.
Put X= LW
And form equation in form of W.
We will get W=20 and L=30
So original area X=LW=30*20=600
Posted from my mobile device
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 above equation we get, L=3/2 W
Plug this value in any of above equation.
Put X= LW
And form equation in form of W.
We will get W=20 and L=30
So original area X=LW=30*20=600
Posted from my mobile device
Posts: 6,727
Updated on: 15 Dec 2020, 07:38
Originally posted by BrentGMATPrepNow on 24 May 2020, 07:16.
Last edited by BrentGMATPrepNow on 15 Dec 2020, 07:38, edited 1 time in total.
Last edited by BrentGMATPrepNow on 15 Dec 2020, 07:38, edited 1 time in total.
Bunuel
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
Posts: 266
A.
Let length = l feet
Let breadth = b 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
Let length = l feet
Let breadth = b 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
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
(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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Expert reply
Posts: 22,740
Bunuel
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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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
\(l(w+5) = lw + 150\)
\(lw + 5l = lw + 150\)
\(l = 30\)
\(w(l+7.5) = lw + 150\)
\(lw + 7.5w = lw + 150\)
\(w = 20\)
\(lw = 20 * 30 = 600\)
Answer is A.
If either the length were increased by 7.5 ft or width were increased by 5 ft = area will be increased by 150
\(l(w+5) = lw + 150\)
\(lw + 5l = lw + 150\)
\(l = 30\)
\(w(l+7.5) = lw + 150\)
\(lw + 7.5w = lw + 150\)
\(w = 20\)
\(lw = 20 * 30 = 600\)
Answer is A.
Bunuel
why is D incorrect? if the length is 10 and 30... the answer would still work
Bunuel
why is D incorrect? if the length is 10 and 30... the answer would still work
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