Question

At most, Alana can spend $40 on carnival tickets. Ride tickets cost $4 each, and food tickets cost $2 each. Alana buys at least 16 tickets. The system of inequalities represents the number of ride tickets, r, and the number of food tickets, f, she buys.

r + f ≥ 16

4r + 2f ≤ 40


What is the maximum number of ride tickets she can buy?

4
6
10
12

Answer 1

4 is the number of ride tickets she can buy

Answer 2

Answer:

The correct option is:  4

Step-by-step explanation:

Given system of inequalities is......

$r+f\geq 16\\ \\ 4r+2f\leq 40$

Taking both inequalities as equations.....

$r+f=16................(1)\\ \\ 4r+2f=40.............(2)$

Multiplying equation (1) by -2, we will get....

$-2(r+f)=-2(16)\\ \\ -2r-2f=-32................(3)$

Now adding equation (2) and (3)..........

$4r+2f=40\\ -2r-2f=-32\\ .............................\\ 2r\ \ \ \ \ \ \ \ \ =8\\ \\ r=\frac{8}{2}=4$

So, the maximum number of ride tickets she can buy is 4.