Question

Pablo mixes 3 units white paint and 1 unit black paint to make gray paint. What two equations show the relationship between units of white paint, w, and units of black paint, b? Show your work.

Answer 1

`w = (1)/(3)b` and
`b = 3w`

Explanation:

Represent white paint with w and black with b

Given

When w = 3; b = 1

Required

Determine the two equations

To get a gray paint, the w and b are needed in the following proportion:

`3 * w = 1 * b` -----(1)

Solve for b

`3 * w = b`

Reorder

`b = 3 * w`

`b = 3w` ---- This is an equation

To get another equation,

Recall that

`3 * w = 1 * b`

Solve for w

`3*w = b`

`3w = b`

Make w the subject

`w = (1)/(3)b`

Hence, the equations that show the relationship between w and b are:

`w = (1)/(3)b` and
`b = 3w`