#29a Word Problems with Two-Step Inequalities - Free Printable

Let's solve the word problem step by step and explain the solution clearly.

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Problem:

Mrs. Treble charges her music students $25 per lesson plus a recital fee of $50. How many lessons can the student take if she pays no more than $175?

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Step 1: Define the variable

Let:
- $ x $ = number of lessons the student takes

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Step 2: Write the inequality

Cost of lessons = $ 25 \times x = 25x $
Recital fee = $ 50 $
Total cost = $ 25x + 50 $

She pays no more than $175, so:

$$
25x + 50 \leq 175
$$

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Step 3: Solve the inequality

Subtract 50 from both sides:

$$
25x \leq 175 - 50
$$
$$
25x \leq 125
$$

Divide both sides by 25:

$$
x \leq \frac{125}{25}
$$
$$
x \leq 5
$$

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Step 4: Interpret the answer

The student can take at most 5 lessons if she wants to pay no more than $175.

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✔ Final Answer:

$$
\boxed{x \leq 5}
$$

So, the student can take up to 5 lessons.

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🔍 Explanation of the steps:

- We used an inequality because the total cost must be less than or equal to $175.
- The recital fee is a one-time charge ($50), added to the per-lesson cost.
- Solving gives us the maximum number of lessons possible within the budget.

✔ This matches the work shown in your image — it's correct!