Question
Multiple Select Question
Justin has $110 to spend at the mall. He wants to buy a hat that costs $25 and a pair of jeans that cost $40. He is also thinking about buying some bags of socks that cost $12 each. There is no tax on any of his purchases.
Which statements are true?
Choose all that apply.
If x is the number of bags of socks Justin can buy, then the inequality representing this situation is x < 3.
If Justin buys the hat and the jeans, solving the inequality 12x + 65 ≤ 110 for x will tell him the maximum number of bags of socks he can buy.
If Justin buys the hat but not the jeans, solving the inequality 12x + 40 ≤ 110 for x will tell him the maximum number of bags of socks he can buy.
If Justin buys the hats, jeans, and the maximum number of bags of socks, he will have enough money left to buy a belt that is on sale for $7.99.
A.
If x is the number of bags of socks Justin can buy, then the inequality representing this situation is x < 3.
B.
If Justin buys the hat and the jeans, solving the inequality 12x + 65 ≤ 110 for x will tell him the maximum number of bags of socks he can buy.
C.
If Justin buys the hat but not the jeans, solving the inequality 12x + 40 ≤ 110 for x will tell him the maximum number of bags of socks he can buy.
D.
If Justin buys the hats, jeans, and the maximum number of bags of socks, he will have enough money left to buy a belt that is on sale for $7.99.
b or d is wrong
Answers
Answered by
GPT-4o mini
Let's evaluate each statement provided in the question to determine their validity.
1. **If x is the number of bags of socks Justin can buy, then the inequality representing this situation is x < 3.**
- If Justin buys the hat ($25) and the jeans ($40), he spends $25 + $40 = $65.
- He has $110 - $65 = $45 left for socks. Each bag of socks costs $12.
- To find the maximum number of bags of socks, we can set up the inequality:
\[
12x \leq 45.
\]
- Solving for x gives:
\[
x \leq \frac{45}{12} \approx 3.75.
\]
- Thus, the maximum integer value of x is 3 (since he can't buy a fraction of a bag). Therefore, **this statement is true**.
2. **If Justin buys the hat and the jeans, solving the inequality 12x + 65 ≤ 110 for x will tell him the maximum number of bags of socks he can buy.**
- As calculated earlier, Justin spends $65 on the hat and jeans. The remaining money for bags of socks is $45.
- Correctly, we should set up the inequality as 12x ≤ 45, not 12x + 65 ≤ 110.
- Thus, the expression 12x + 65 ≤ 110 is incorrect for determining how many bags of socks he can buy. Therefore, **this statement is false**.
3. **If Justin buys the hat but not the jeans, solving the inequality 12x + 40 ≤ 110 for x will tell him the maximum number of bags of socks he can buy.**
- If Justin buys the hat only, he spends $25. This leaves him with $110 - $25 = $85.
- Setup the inequality:
\[
12x \leq 85,
\]
- Simplifying it gives:
\[
x \leq \frac{85}{12} \approx 7.08,
\]
- Thus, the maximum integer value of x is 7. Using 12x + 40 in this context leads to an incorrect calculation, as he would not be spending $40 since he did not buy the jeans. Therefore, **this statement is false**.
4. **If Justin buys the hat, jeans, and the maximum number of bags of socks, he will have enough money left to buy a belt that is on sale for $7.99.**
- If he buys the hat and jeans, he spends $65, and we've calculated he can buy a maximum of 3 bags of socks, totaling:
\[
3 \times 12 = 36.
\]
- The total spent is:
\[
65 + 36 = 101.
\]
- Money left after these purchases is:
\[
110 - 101 = 9.
\]
- He can buy the belt for $7.99 with the $9 left. Therefore, **this statement is true**.
### Summary
- **True Statements**: A and D.
- **False Statements**: B and C.
So, B or D being wrong is incorrect. Instead, B and C are wrong.
1. **If x is the number of bags of socks Justin can buy, then the inequality representing this situation is x < 3.**
- If Justin buys the hat ($25) and the jeans ($40), he spends $25 + $40 = $65.
- He has $110 - $65 = $45 left for socks. Each bag of socks costs $12.
- To find the maximum number of bags of socks, we can set up the inequality:
\[
12x \leq 45.
\]
- Solving for x gives:
\[
x \leq \frac{45}{12} \approx 3.75.
\]
- Thus, the maximum integer value of x is 3 (since he can't buy a fraction of a bag). Therefore, **this statement is true**.
2. **If Justin buys the hat and the jeans, solving the inequality 12x + 65 ≤ 110 for x will tell him the maximum number of bags of socks he can buy.**
- As calculated earlier, Justin spends $65 on the hat and jeans. The remaining money for bags of socks is $45.
- Correctly, we should set up the inequality as 12x ≤ 45, not 12x + 65 ≤ 110.
- Thus, the expression 12x + 65 ≤ 110 is incorrect for determining how many bags of socks he can buy. Therefore, **this statement is false**.
3. **If Justin buys the hat but not the jeans, solving the inequality 12x + 40 ≤ 110 for x will tell him the maximum number of bags of socks he can buy.**
- If Justin buys the hat only, he spends $25. This leaves him with $110 - $25 = $85.
- Setup the inequality:
\[
12x \leq 85,
\]
- Simplifying it gives:
\[
x \leq \frac{85}{12} \approx 7.08,
\]
- Thus, the maximum integer value of x is 7. Using 12x + 40 in this context leads to an incorrect calculation, as he would not be spending $40 since he did not buy the jeans. Therefore, **this statement is false**.
4. **If Justin buys the hat, jeans, and the maximum number of bags of socks, he will have enough money left to buy a belt that is on sale for $7.99.**
- If he buys the hat and jeans, he spends $65, and we've calculated he can buy a maximum of 3 bags of socks, totaling:
\[
3 \times 12 = 36.
\]
- The total spent is:
\[
65 + 36 = 101.
\]
- Money left after these purchases is:
\[
110 - 101 = 9.
\]
- He can buy the belt for $7.99 with the $9 left. Therefore, **this statement is true**.
### Summary
- **True Statements**: A and D.
- **False Statements**: B and C.
So, B or D being wrong is incorrect. Instead, B and C are wrong.
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