Jane plans to purchase three pairs of slacks all costing the same amount, and a blouse that is $4 cheaper than one of the pairs of slacks. She has $75 to spend but wants to have at least $3 left. What is the price range for the slacks?

Let the price of one pair of slacks be denoted by $ x $. Therefore, the total cost of the three pairs of slacks would be $ 3x $. The price of the blouse is $4 cheaper than one pair of slacks, so the blouse costs $ x - 4 $.

### Total spending equation:
The total amount Jane will spend on the slacks and the blouse is:
\[
3x + (x - 4)
\]
This simplifies to:
\[
4x - 4
\]

Jane has $75 but wants to have at least $3 left, so she can spend at most $ 75 - 3 = 72 $.

### Inequality:
\[
4x - 4 \leq 72
\]

Now, solve for $ x $:
\[
4x - 4 \leq 72
\]
\[
4x \leq 76
\]
\[
x \leq 19
\]

Thus, the price of one pair of slacks must be less than or equal to $19. To make sure the blouse is not free or negative in price, we also need $ x - 4 > 0 $, meaning $ x > 4 $.

### Final Answer:
The price range for each pair of slacks is:
\[
4 < x \leq 19
\]

Would you like more details or have any other questions?

Here are some related questions to deepen your understanding:
1. What if Jane had $90 and still wanted $3 left? What would the price range be?
2. How would the situation change if the blouse were $2 cheaper than the slacks instead of $4?
3. What would the total cost be if each pair of slacks cost $15?
4. If Jane bought four pairs of slacks instead, how would that affect the inequality?
5. How would you solve this problem if Jane wanted to spend all her money?

**Tip:** Always set up inequalities carefully when dealing with budget constraints to make sure all conditions are met.

Solve a real-world algebra problem where Jane buys three pairs of slacks and a blouse, with budget constraints. This step-by-step solution involves setting up and solving inequalities to find the price range for each pair of slacks. Suitable for students in Grades 7-9.

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