Question

Caleb has $37 and wants to purchase movie tickets for him and some of his friends. He also wants to buy a large popcorn for the group to share. The following inequality represents the cost of the tickets, where x is the number of tickets. 8x+5≤37 Which answer correctly interprets the inequality?

A) Caleb can buy up to 4 movie tickets, and the inequality ensures he has enough money for a large popcorn.

B) Caleb can buy up to 5 movie tickets, and the inequality ensures he has enough money for a large popcorn.

C) Caleb can buy up to 6 movie tickets, and the inequality ensures he has enough money for a large popcorn.

D) Caleb cannot afford any movie tickets and a large popcorn with the given amount of money.

Answer 1

Caleb can purchase up to 4 movie tickets along with a large popcorn without exceeding his budget of $37. The inequality 8x + 5 ≤ 37 was used to find the maximum number of tickets he can afford.

Step-by-step explanation:

The inequality Caleb is working with is 8x + 5 ≤ 37, where x represents the number of movie tickets he can purchase and 5 represents the cost of the large popcorn. To determine how many tickets he can buy, he must ensure the total cost does not exceed $37.

First, subtract the cost of the large popcorn from the total amount of money Caleb has:

37 - 5 = 32

Now, divide the remaining amount by the cost of one movie ticket, which is $8:

32 ÷ 8 = 4

Therefore, Caleb can buy up to 4 movie tickets and still have enough to purchase the large popcorn. This fits the budget constraint similar to what we see in economics where individuals must choose combinations of goods that fit within their budget.