Question 155758: If you would please help me solve this word problem:
The length of a rectangle is 1 inch less than three times the width. If the length is increased by 6 inches and the width is increased by 5 inches, then the length will be twice the width. Find the dimensions of the rectangle.
So far this is what I have done: Let x=the width
Since the length = 3x-1, I added the 6 inches and double the width.
I have for an equation:
(3x-1)+6 = 2x
However when I solved it it turned out to be:
3x+5=2x
x+5=0
x=-5
But, as you can see, I can't have a negative dimension in a rectangle! D:!!
So please, can you point out what I did wrong ;-;? Please and thank you!
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let L = length and W = width.
L = 3W-1 and
L+6 = 2(W+5) Substitute the L from the above equation.
(3W-1)+6 = 2(W+5) Simplify.
3W+5 = 2W+10 Subtract 2W from both sides.
W+5 = 10 Subtract 5 from both sides.
W = 5 inches and
L = 3W-1
L = 3(5)-1
L = 15-1
L = 14 inches.
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