To determine the maximum number of packages of stickers Emma can buy, we first need to analyze her available funds after her expenses.
- Total amount available: $26
- Amount spent on the book: $12.81
- Amount set aside for lunch: $10.00
We can calculate her remaining amount (R) after these expenses:
\[ R = 26 - 12.81 - 10.00 \]
Now let’s compute \(R\):
\[ R = 26 - 12.81 - 10.00 = 26 - 22.81 = 3.19 \]
Now, we need to express her remaining funds in terms of the number of sticker packages (p) she can buy, where each package costs $0.42. The inequality that represents this scenario is:
\[ 0.42p \leq R \]
Substituting \(R\) with $3.19 gives us:
\[ 0.42p \leq 3.19 \]
To answer the questions provided:
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The correct inequality to use is \(0.42p + 22.81 \leq 26\), which means 0.42p + 22.81 ≤ 26 (considering this translates her total budget after subtracting known expenses).
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The maximum number of packages Emma can buy can be calculated by solving:
\[ p \leq \frac{3.19}{0.42} \]
Calculating:
\[ p \leq 7.5952 \]
Since she can only buy whole packages, we take the maximum whole number, which is \(p = 7\).
Thus, the answers are:
- The inequality is 0.42p + 22.81 ≤ 26.
- The maximum number of packages Emma can buy is 7.