A school would like to hire a magician to put on 1-hour shows at the school carnival. The magician charges $100 for set-up and take-down, plus $175 for each show that they perform. The school can spend at most $750 on the magician.

What is the greatest number of shows that the school can afford to hire the magician?

Complete the sentence below by selecting the correct answer from the drop down.

Let's solve the problem step by step.

The total cost for hiring the magician consists of:
- A fixed cost of $100 for set-up and take-down.
- $175 for each show performed.

The school can spend at most $750 on the magician. We need to find the greatest number of shows the school can afford, given this budget constraint.

Let $ x $ be the number of shows the school can hire. The total cost is given by:
\[
\text{Total Cost} = 100 + 175x
\]
We know the total cost should not exceed $750, so we set up the inequality:
\[
100 + 175x \leq 750
\]
Now, solve for $ x $:

1. Subtract 100 from both sides:
\[
175x \leq 750 - 100
\]
\[
175x \leq 650
\]

2. Divide both sides by 175:
\[
x \leq \frac{650}{175}
\]
\[
x \leq 3.71
\]

Since $ x $ must be a whole number, the greatest integer $ x $ can be is 3.

Thus, the greatest number of shows the school can afford is **3**.

---

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the total cost change if the magician charged more per show?
2. What if the school increased their budget to $1000? How many shows could they afford?
3. How would the answer change if the set-up and take-down fee were $150 instead of $100?
4. How can you set up and solve similar inequalities for other budgeting problems?
5. What if the magician offered a discount for each additional show?

**Tip:** Always make sure to express constraints (like budgets) as inequalities to understand the limits of what can be afforded!

A school would like to hire a magician to put on 1-hour shows at the school carnival. The magician charges $100 for set-up and take-down, plus $175 for each show that they perform. The school can spend at most $750 on the magician. What is the greatest number of shows that the school can afford to hire the magician?

Solve a budgeting problem where a school wants to hire a magician for 1-hour shows, given setup costs and a budget constraint. Learn to solve linear inequalities and calculate the maximum number of shows. Suitable for Grades 6-8, this exercise covers algebraic concepts and inequality solving.

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