the original piece of wood

Question

a painting is stretched over a rectangular wooden frame whose length is two and a half times its width in feet.  The sum of the length and the width is 7 feet. The wood for the frame came from one piece that was cut into four pieces.  How long was the original piece of wood in feet?

Answer 1

Write down what you are given and see what you have.  Let l = length and w = width

l = 2 1/2 w

l + w = 7

Substitute l = 2 1/2 w into second equation.  

2 1/2 w + w = 7

3 1/2 w = 7  Make 3 1/2 into improper fraction 7/2

7/2 w = 7   multiply each side by 2/7

w = 2

Substitute it back into the equation to find l.

l + w = 7

l + 2 = 7

l = 5