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

http://media.education2020.com/evresources/3109/3109-05/3109-05-10/3109-05-10-assessment/3109-05-10-23.png

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

4
6
10
12

Answer 1

Alright, so in order to figure the maximum amount of ride tickets, optimally, you would want to spend all $40 on ride tickets, so the answer would be 10 ride tickets.
However, you must have 16 tickets at a minimum, so that would mean you would want to buy at least 6 food tickets right? But if you bought 6 food tickets, that would mean you already spent $12 dollars NOT on ride tickets. That would leave $28 dollars, which would be 7 ride tickets, and 7 ride tickets + 6 food tickets = 13. So in that case you must buy even more food tickets to make up the difference.
So if you say bought only 6 ride tickets ($24), then the remaining amount of money would be ($26), which would be enough for 13 food tickets. 13 + 6 = 19, which means that this solution works.
Therefore the maximum ride tickets she should buy would be 6.