Question
A piece of paper measures 8.5 inches by 11 inches. Mrs. Wickowitz wants to hang paper on a bulletin board that has a height of 24 inches and an area of 1,728 square inches. Which inequality best represents the possible whole numbers of papers, p, that Mrs. Wickowitz could hang?
p ≤ 12
p ≤ 16
p ≤ 18
p ≤ 24
p ≤ 12
p ≤ 16
p ≤ 18
p ≤ 24
Answers
Answered by
GPT-4o mini
To determine how many pieces of paper Mrs. Wickowitz can hang on the bulletin board, we need to calculate the area of the paper and the area of the bulletin board, then determine how many pieces of paper can fit within that area.
1. **Calculate the area of one piece of paper:**
- We have a piece of paper that measures 8.5 inches by 11 inches.
- Area of one piece of paper = width × height = 8.5 inches × 11 inches = 93.5 square inches.
2. **Calculate the area of the bulletin board:**
- The bulletin board has an area of 1,728 square inches (as given).
3. **Determine the maximum number of pieces of paper that can fit on the bulletin board:**
- To find the maximum number of whole pieces of paper that can fit, we divide the area of the bulletin board by the area of one piece of paper:
\[
\text{Maximum number of papers} = \frac{\text{Area of bulletin board}}{\text{Area of one piece of paper}} = \frac{1728 \text{ square inches}}{93.5 \text{ square inches}}.
\]
- Calculating this gives:
\[
\frac{1728}{93.5} \approx 18.5.
\]
- Since we can only hang whole pieces of paper, we take the integer part, which is 18.
4. **Establishing the inequality:**
- Therefore, the maximum number of pieces of paper, \( p \), that Mrs. Wickowitz can hang is 18. This can be represented by the inequality:
\[
p \leq 18.
\]
Thus, the correct answer is:
**p ≤ 18**.
1. **Calculate the area of one piece of paper:**
- We have a piece of paper that measures 8.5 inches by 11 inches.
- Area of one piece of paper = width × height = 8.5 inches × 11 inches = 93.5 square inches.
2. **Calculate the area of the bulletin board:**
- The bulletin board has an area of 1,728 square inches (as given).
3. **Determine the maximum number of pieces of paper that can fit on the bulletin board:**
- To find the maximum number of whole pieces of paper that can fit, we divide the area of the bulletin board by the area of one piece of paper:
\[
\text{Maximum number of papers} = \frac{\text{Area of bulletin board}}{\text{Area of one piece of paper}} = \frac{1728 \text{ square inches}}{93.5 \text{ square inches}}.
\]
- Calculating this gives:
\[
\frac{1728}{93.5} \approx 18.5.
\]
- Since we can only hang whole pieces of paper, we take the integer part, which is 18.
4. **Establishing the inequality:**
- Therefore, the maximum number of pieces of paper, \( p \), that Mrs. Wickowitz can hang is 18. This can be represented by the inequality:
\[
p \leq 18.
\]
Thus, the correct answer is:
**p ≤ 18**.