Question

A group of friends is going to a baseball game. They have a total budget of $100.00 to spend. The game tickets cost $87.50 and each soda drink costs $2.00 each. Write an inequality where x is the number of drinks the group of friends could buy in all, with their ticket costs and budget.

a) x + 87.50 + 2x ≤ 100
b) x + 87.50 + 2x ≥ 100
c) x + 87.50 - 2x ≤ 100
d) x + 87.50 - 2x ≥ 100

Answer 1

The correct inequality to represent the number of soda drinks the group can buy is option a) x + 87.50 + 2x ≤ 100, which simplifies to 3x + 87.50 ≤ 100 and further reduces to 3x ≤ 12.50.

Step-by-step explanation:

The group of friends needs to calculate how many soda drinks they can purchase with their remaining budget after buying game tickets. The price for the game tickets is fixed at $87.50, and each soda costs $2.00. Since they have a total budget of $100.00, we can write an inequality to represent the maximum number of drinks (x) they can buy without exceeding their budget.

The inequality that represents the situation is:

a) x + 87.50 + 2x ≤ 100

To solve for the number of drinks, you would combine like terms, which gives you 3x + 87.50 ≤ 100. Subtract 87.50 from both sides of the inequality to isolate the x term, yielding 3x ≤ 12.50, and finally divide by 3 to find the maximum number of drinks they can afford. Therefore, the inequality correctly showing the number of soda drinks the group can buy is option a).