Question

James brought 30 dollars to the arcade, which has an admission fee of 7 dollars. Each token at the arcade cost an additional 50 cents. Write an inequality used to solve for t the number of tokens he can purchase from the arcade, and what is the maximum number of tokens that he can buy.

Answer 1

James can buy a maximum of 46 tokens at the arcade after paying a $7 admission fee from his $30 budget. The inequality for the number of tokens t he can buy is 7 + 0.5t <= 30.

Step-by-step explanation:

To solve for the number of tokens t that James can purchase at the arcade, we need to consider both the admission fee and the cost per token. Since the admission fee is $7 and each token costs $0.50, we can write an inequality that represents the maximum number of tokens t that James can buy with his $30. The inequality would look like this:

• 7 + 0.5t ≤ 30

This inequality states that the total amount spent on the admission fee and the tokens cannot exceed $30. To find the maximum number of tokens t, we subtract the admission fee from the total amount of money James has and then divide by the cost per token:

1. Subtract the admission fee from the total budget: $30 - $7 = $23
2. Divide the remaining money by the cost per token: $23 / $0.50 = 46

Therefore, James can buy a maximum of 46 tokens at the arcade with his $30, after the admission fee.