Emma has $26 for her weekend expenses. She spent $12.81, including tax, on a new book. Additionally, she needs to set aside $10.00 for a lunch outing next week. If stickers cost $0.42 per package, tax included, describe the maximum number of packages (p) Emma can buy. a b c or d

Question

Which inequality should be used to solve this problem?

(1 point)
Responses

0.42p + 2.81 ≥ 26
0.42p + 2.81 ≥ 26

0.42p + 2.81 ≤ 26
0.42p + 2.81 ≤ 26

0.42p + 22.81≤ 26
0.42p + 22.81≤ 26

0.42p + 22.81≥ 26
0.42p + 22.81≥ 26
Question 2
(1 point)
The maximum number of packages Emma can buy is
.

Answer 1

To determine the inequality that should be used to solve the problem, we first need to assess Emma's financial situation:

1. Total money available: $26
2. Money spent on the book: $12.81
3. Money set aside for lunch: $10.00

Next, we need to calculate the amount of money Emma has left after these expenses:

• Money left after buying the book: \( 26 - 12.81 = 13.19 \)

• Money left after setting aside for lunch: \( 13.19 - 10 = 3.19 \)

So, Emma has $3.19 left to spend on stickers.

Now, we let \( p \) represent the number of packages of stickers she can buy. Each package costs $0.42, so the total cost for \( p \) packages is \( 0.42p \).

Setting up the inequality for her spending:

\[ 0.42p \leq 3.19 \]

To see which option corresponds to this situation, we rearrange it:

• Subtract $2.81 from both sides to account for the initial outlay directly: \[ 0.42p + 2.81 \leq 26 \]

Thus, the correct inequality to use would be:

0.42p + 2.81 ≤ 26

For Question 2

To find the maximum number of packages \( p \):

1. Solve the inequality: \[ 0.42p \leq 3.19 \] \[ p \leq \frac{3.19}{0.42} \] \[ p \leq 7.595 \]

Since \( p \) must be a whole number, the maximum number of packages Emma can buy is 7.

Summary:

• The appropriate inequality is: 0.42p + 2.81 ≤ 26
• The maximum number of packages Emma can buy is 7.