Question

When jack bought his new truck, there were 96 different ways his truck could be equipped. He had four choices of engines and two choices of transmissions. If only other choice was color, how many colors were available?

Answer 1

There are 12 colors available

Explanation:

We have product rule which states that if there are
`n_(1)` ways of doing one task, and
`n_(2)` ways of doing another task then there
`n_(1)n_(2)` ways of doing the tasks together.

Let us assume that there are x choices for colors

so we have 4 ways of selecting engines , 2 ways of selecting transmissions and x ways of selecting colors

number of ways of truck could be equipped =
`4*2*x`

=
`8x`

it is given that number of ways truck could be equipped=
`96`

so we have

`8x= 96`

`x=(96)/(8)` ( divide both side by 8)

`x= 12`

There are 12 colors available

Answer 2

To Find all the different ways the truck could be, you would mutiply all the choices together.

There were three different choices.

Multiply the two known ones together than divide the total different ways by that to find the third choice.

4 x 2 = 8

96 / 8 = 12

There are 12 colors available.