A box has a length of 6x inches. The width is 1/3 the length and the height is 1/2 the length. If the volume equals 972 cubic inches, what does x equal?

Question

Multi step problems for grade 7

Answer 1

Justin, try this approach:

 

1. formula for volume = Length * width * heighth = 972 cubic inches

 

2. Width = Length ÷3

 

3. Height =  Length ÷2

 

4. Length = 6 X inches

 

Substitute equations 2-4 into equation 1 giving us

 

972 cubic inches = (6X)*(6X ÷3)*(6X ÷2) = 6³X³÷6

 

972 cubic inches =  6²X³

 

972 ÷ 36 =  X³

 

972 ÷ 36 = X³

 

27 = X³

 

27^1/3 = X or find the cube root of 27

 

X = 3

 

Length = 6*3 = 18

Width = 18÷3 = 6

Height = 18÷2 = 9

Volume = 18* 6* 9= 972 cubic inches

Hope that helps