Question

The function p(x) = 2x +1 determines how many pizzas need to be purchased for an after school meeting, where x is the number of students at the meeting. The club leader uses r(p(x)) to find the amount of money to bring for the pizza purchase. The function r(x) = 4x − 3. Solve for how much money to bring when there are 9 students in the meeting.

Answer 1

`p(x) = 2x + 9`
substitute the given number of students in the meeting


`p(x) = 2(9) + 9`

`r(p(x))`
wherever there is an x in the equation of r(x) substitute the p(x) equation

`r(x) = 4x - 3`


`4(2(9) + 9) - 3`

`4(18 + 9) - 3`

`4(27) - 3`

`108 - 3 = 105`

Answer 2

r(p(x))=73

Explanation:

To find the value of r(p(x)), the equation for p(x) which is 2x + 1, is substituted into every place that there is a x in the equation of r(x).

`r(x)=4x-3\\r(p(x))=4(2x+1)-3\\r(p(x))=8x+4-3\\r(p(9))=8(9)+4-3\\r(p(9))=73`