find the length width and height of the box

Question

the sum of the length, width, and height of a rectangular box is 16cm, the width is twice the height, and twice the length exceeds the sum of the width and height by 5. Find the length width and height of the box

Answer 1

There are two challenges here, I don't know which is giving you a problem. Translating word problems into equations is tricky for some folks. If that's what's bothering you, here is the translation.

L + W + H = 16
W = 2H
2L = W + H + 5

If the hard part is solving these three equations, let's start by substituting 2H for W

L + 2H + H = 16
=> L + 3H = 16
2L = 2H + H + 5
=> 2L = 3H + 5

Now solve one equation for L

L = 16 - 3H

And substitute that into the other equation
2 ( 16-3H) = 3H + 5
=> 32 - 6H = 3H + 5

Now solve for H
32 - 5 = 9H
9H = 27
H = 3

Substitute back into the L equation
L = 16 - 3*3
=> L = 16-9 = 7

Finally substitute back into the equation for W
W = 2H
=> W = 2 * 3 = 6

Result: W = 6, H = 3, L = 7

Answer 2

Let h = the height of the box

Let 2h = the width

Let h + 2h + 5 = the length

             2

 

h + 2h + 3h + 5 = 16       

                    2

3h + 3h + 5  = 16       Multiply both sides of the equation by 2.

              2

6h + 3h + 5 = 32

9h = 27

h = 3

height = 3 cm

width = 6 cm

length = 3(3) + 5 = 14/2 = 7 cm

                  2