If its length is decreased by 7 and its width is increased by 5, a square is formed. How long is the rectangle?
First break this down into 2 mathematical equations:
First equation:
L = 3W + 2 (the length is 2 more than 3 times the width)
Second equation:
L - 7 = W + 5 (length decreased by 7 equals the width increased by 5)
So we have 2 equations and 2 unknowns - substitute one into the other to give you:
L = 17
W = 5
Therefore the length is 17.
Let the width of the rectangle be x, and then the length would be 2+3x since it is 2 more than 3 times.
The width of the square is x + 5, since you increase it by 5, and the length is 2+3x-7 since you decrease it's length by 7.
But a squares width and length are the same, hence:
2+3x-7 = x+5
3x-5= x+5
2x = 10
x = 5
Now to find how long the rectangle is, simply sub x = 5 into the previous rectangles length, which was 2+3x.
Therefore the length of the rectange is 17 units.
We know:
L = 3W+2
and
L-7 = W+5
Solve for L:
W = L-12
L = 3(L-12) + 2
L = 3L -36 + 2
2L = 34
L = 17 (and, as a check, W = 5, which checks out).
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Verified answer
First break this down into 2 mathematical equations:
First equation:
L = 3W + 2 (the length is 2 more than 3 times the width)
Second equation:
L - 7 = W + 5 (length decreased by 7 equals the width increased by 5)
So we have 2 equations and 2 unknowns - substitute one into the other to give you:
L = 17
W = 5
Therefore the length is 17.
Let the width of the rectangle be x, and then the length would be 2+3x since it is 2 more than 3 times.
The width of the square is x + 5, since you increase it by 5, and the length is 2+3x-7 since you decrease it's length by 7.
But a squares width and length are the same, hence:
2+3x-7 = x+5
3x-5= x+5
2x = 10
x = 5
Now to find how long the rectangle is, simply sub x = 5 into the previous rectangles length, which was 2+3x.
Therefore the length of the rectange is 17 units.
We know:
L = 3W+2
and
L-7 = W+5
Solve for L:
W = L-12
L = 3(L-12) + 2
L = 3L -36 + 2
2L = 34
L = 17 (and, as a check, W = 5, which checks out).