Anna and her children went into a grocery store and will buy apples and peaches. Each apple costs $0.75 and each peach costs $1.25. Anna has a total of $20 to spend on apples and peaches. Write an inequality that would represent the possible values for the number of apples purchased, a,a, and the number of peaches purchased, p, .p.

To represent the possible values for the number of apples and peaches Anna can purchase, we need to create an inequality that accounts for the total cost of both the apples and peaches, while ensuring that the total does not exceed $20.

Each apple costs $0.75, and Anna purchases $ a $ apples. Therefore, the cost of the apples is $ 0.75a $.

Each peach costs $1.25, and Anna purchases $ p $ peaches. Therefore, the cost of the peaches is $ 1.25p $.

Since Anna has $20 to spend, the total cost of apples and peaches should be less than or equal to $20.

The inequality is:

\[
0.75a + 1.25p \leq 20
\]

This inequality represents the relationship between the number of apples $ a $ and peaches $ p $ that Anna can purchase given her budget.

### Do you want more details or have any other questions?

Here are some follow-up questions for further exploration:
1. What is the maximum number of apples Anna can buy if she buys no peaches?
2. What is the maximum number of peaches Anna can buy if she buys no apples?
3. Can Anna buy 10 apples and 8 peaches within her budget?
4. What is the equation if the prices of apples and peaches increase by 10%?
5. How would the inequality change if Anna has $25 instead of $20?

**Tip:** When solving inequality word problems, always identify the cost per item and set up the inequality based on the total budget!

Anna and her children went into a grocery store and will buy apples and peaches. Each apple costs $0.75 and each peach costs $1.25. Anna has a total of $20 to spend on apples and peaches. Write an inequality that would represent the possible values for the number of apples purchased, a, and the number of peaches purchased, p.

Learn how to represent a real-world scenario involving budget constraints with a linear inequality. This problem covers key algebraic concepts like inequalities and linear equations, perfect for students in Grades 6-8.

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