translate the given information into a system of equation the question is at the description

Question

it is the question please help me.

1.the sum of the length,width,height of a rectangular box is 17 cm.twice the width exceeds the height by 1.the sum of the length and the width is shorter than the height by the by 1cm. find the length,length,width and height of the box.

Answer 1

Three unknowns means three equations must be written.

 

1) l (length) + w(width) + h(height) = 17

2) 2w - 1 = h

3) l + w + 1 = h

 

Let h = h, so 2w - 1 = l + w +1

                     w - 1 = l + 1

                     w = l + 2

From eq. #3 above, l + w + 1 = h

Substitute: l + l + 2 + 1  = h

                2l + 3 = h

So, 2l +3 = 17 - l - w (from eq #1 above)

      3l + 3 = 17 - w

      3l = 14 - w

Substitute: 3l = 14 - l - 2 (from  w = l + 2 above)

                 4l = 12

                  l = 3 First answer

 

w = l + 2 from above in bold.  So, if l = 3, then w = 5  Second answer

 

If l + w + h = 17 ( eq #1 above), then 3 + 5 + h = 17, and h = 9