SOLUTION: The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. What is

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Question 753277: The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. What is the area of the original rectangle?
12 in^2
48 in^2
96 in^2
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
EDIT: MISREAD "DECREASED". NOW GIVING PROPER RESULT

w for width and y for length
w=2n and y=2n%2B2

Then w-3=2n-3 is used and the area becomes 24 square inches.

%282n-3%29%282n%2B2%29=24
4n%5E2-6n%2B4n-6=24
4n%5E2-2n-30=0
highlight%282n%5E2-n-15=0%29

n=%281%2B-+sqrt%281-4%2A2%2A%28-15%29%29%29%2F4
n=-5%2F4 or highlight%28n=3%29.

Taking the positive value for n,
original figure, w=6 and length=8.
Original area is highlight%286%2A8=48%29 square inches.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. What is the area of the original rectangle?
12 in^2
48 in^2
96 in^2

Let the width be the smaller integer of W
Then length = W + 2

If width is decreased by 3, it becomes: W - 3
Therefore, new width, times original length, equals given area, OR

(W - 3)(W + 2) = 24

W%5E2+-+W+-+6+=+24

W%5E2+-+W+-+6+-+24+=+0

W%5E2+-+W+-+30+=+0

(W + 5)(W - 6) = 0

W, or width = - 5(ignore), or 6

Length, therefore = 8 (6 + 2)

Area of original rectangle = 6 * 8, or highlight_green%2848_square_inches%29

You can do the check!!

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