Question

The members of the student council are trying to raise $500 for charity. They paid $150 for decorations and will be able to save $8 from every homecoming ticket they sell. The inequality 8t - 150 ≥ 500 can be used to determine the number of tickets (t) they need to sell to reach their goal.

Which statement about the number of tickets they need to sell to raise at least $500 is true?

a) They need to sell fewer than 10 tickets.
b) They need to sell more than 10 tickets.
c) They need to sell at least 10 tickets.
d) They need to sell exactly 10 tickets.

Answer 1

The student council needs to sell at least 82 tickets to meet their fundraising goal of $500 after expenses. They will exceed their initial goal by solving the inequality, confirming that they need to sell at least 10 tickets.

Step-by-step explanation:

The members of the student council need to solve the inequality 8t - 150 ≥ 500 to find the number of homecoming tickets (t) they need to sell to reach their charity goal of at least $500, after having paid $150 for decorations. Solving the inequality:

1. Add 150 to both sides: 8t ≥ 650.
2. Divide both sides by 8 to find t: t ≥ 81.25.

Since the student council cannot sell a fraction of a ticket, they need to round up to the nearest whole number. Therefore, they need to sell at least 82 tickets to reach their goal. This means that statement (c) is true: They need to sell at least 10 tickets.