Question

The number of teams who entered in a 3-on-3 charity basketball tournament can be modeled by function T, where x is the number of years since the tournament first started.

T(x)=4x+24

The entry fee paid by each team to enter the tournament can be modeled by function F, where x is the number of years since the tournament first started.

F(x)=5x+45

Which function, R, best represents the total entry fees collected in the xth year since the tournament first started?

A. r(x)=20x^2+300x+1,080

B. r(x)=9x+69

C. r(x)=9x^2+29x+69

D. r(x)=20x^2+1,080

Answer 1

Option A:

`R(x)=20x^2+300x+1080`

Step-by-step explanation:

The revenue, R(x) is the product of the number of teams who entered the tournament, T(x), times the entry fee paid by each team, F(x); then you can write:

• 
  `R(x)=T(x)* F(x)`

Thus you must multiply the two functions (polynomials):

• 
  `R(x)=(4x+24)* (5x+45)`

Use distributive property:

`R(x)=(4x+24)* (5x+45)=(4x)(5x)+(4x)(45)+(24)(5x)+(24)(45)`

Simplify:

`R(x)=(4x)(5x)+(4x)(45)+(24)(5x)+(24)(45)=20x^2+180x+120x+1080`

Add like terms:

`R(x)=20x^2+180x+120x+1080=20x^2+300x+1080`