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

Answer:

• $R(x)=20x^2+300x+1080$

Explanation:

1. Number of teams

$T(x)=4x+24$

• T(x): number of teams

• x: number of years since the tournament first started

2. Fee

$F(x)=5x+45$

• F(x): entry fee paid by each team

• x: number of years since the tournament first started

3. Total entry fees

• Total entry fees = number of teams × fee paid by the by each team

$R(x)=T(x)\cdot F(x)\\ \\ R(x)=(4x+24)\cdot (5x+45)\\ \\ R(x)=(4x)\cdot (5x)+(4x)\cdot (45)+(24)\cdot (5x)+(24)(45)\\ \\ R(x)=20x^2+180x+120x+1080\\ \\ R(x)=20x^2+300x+1080$