Hi Stephanie,
Rather than do your homework problem for you I am going to solve a similar problem.
A rectangle has a length that is 5 cm less than three times the width. The area of the rectangle is 250 cm squared. Find the dimensions of the rectangle.
I am going to use L for the length of the rectangle and W for the width. I know that L is 5 cm less than three times W so
L is 5 cm less than 3W, that is
L = 3W  5
I also know that the area is 250 cm squared and the area of a rectangle is the length times the width. Thus
L W = 250, that is
(3W  5) W = 250
Expanding this I get
3W^{2}  5W = 250, or
3W^{2}  5W  250 = 0
Factoring I get
(3W + 25)(W  10) = 0
Thus W = ^{25}/_{3} or W = 10
Since W is the width of a rectangle it can't be negative and hence W = 10 cm.
Since L = 3W  5, L = 30  5 = 25 cm.
Now check:
Is the length that is 5 cm less than three times the width? Yes, 25 cm is 5 cm less that 3 times 10 cm.
Is the area of the rectangle is 250 cm squared? Yes, L W = 10 25 = 250 cm squared.
Now try your problem and make sure you check your answer.
Penny
