To determine the maximum number of sticker packages (p) Emma can buy, let's break down her expenses.
- Emma started with $26.
- She spent $12.81 on a book.
- She needs to set aside $10.00 for lunch next week.
Now, let's calculate how much money Emma has left for buying stickers:
Total amount: $26.00
Amount spent on the book: $12.81
Amount set aside for lunch: $10.00
Remaining amount for stickers = Total amount - Amount spent on book - Amount set aside for lunch
Remaining amount for stickers = $26.00 - $12.81 - $10.00
Remaining amount for stickers = $26.00 - $22.81
Remaining amount for stickers = $3.19
Now, the cost of each sticker package is $0.42. Therefore, we need to set up an inequality based on how many packages Emma can buy with the remaining amount:
0.42p ≤ 3.19
This simplifies to:
p ≤ 3.19 / 0.42
Now, let's review the options provided for the inequality:
- 0.42p + 2.81 ≥ 26
- 0.42p + 22.81 ≤ 26
- 0.42p + 22.81 ≥ 26
- 0.42p + 2.81 ≤ 26
Looking at our calculations, we know that the amount left for stickers is part of the equation:
0.42p ≤ 3.19
This doesn't exactly match any of the options directly. However, because we need to ensure that we account for her total money (which is $26) minus what she's already spent ($12.81) and saved ($10.00), we could rewrite it accordingly.
Given the closest match, the correct inequality that can be derived from her remaining budget is 0.42p + 22.81 ≤ 26, since 22.81 is the total spent and reserved, and the other costs must be less than or equal to her starting amount of $26.
So, the answer to the question regarding the inequality is: 0.42p + 22.81 ≤ 26
Now, to find out the maximum number of packages (p):
Convert the inequality:
0.42p ≤ 3.19
Calculate p:
p ≤ 3.19 / 0.42 ≈ 7.595
Since Emma can't buy a fraction of a package, she can buy a maximum of 7 packages.
Thus, the maximum number of packages Emma can buy is 7.