Question
Luis has $12 and wants to buy 6.6 pounds of apples. Apples cost $1.80 per pound. Luis rounded each value and estimated that he does not have enough money to cover the cost of the apples before sales tax is applied. Which best explains how his estimate relates to the actual product?
Because each value rounds up, his estimate is higher than the actual product. He might have enough money to buy the apples.
Because each value rounds up, his estimate is higher than the actual product. He does not have enough money to buy the apples.
Because each value rounds up, his estimate is lower than the actual product. He does not have enough money to buy the apples.
Because each value rounds up, his estimate is lower than the actual product. He might have enough money to buy the apples.
Because each value rounds up, his estimate is higher than the actual product. He might have enough money to buy the apples.
Because each value rounds up, his estimate is higher than the actual product. He does not have enough money to buy the apples.
Because each value rounds up, his estimate is lower than the actual product. He does not have enough money to buy the apples.
Because each value rounds up, his estimate is lower than the actual product. He might have enough money to buy the apples.
Answers
GPT-4o mini
To analyze Luis's situation, let's first calculate the actual cost of the apples without rounding.
The cost of apples is $1.80 per pound, and he wants to buy 6.6 pounds:
\[
\text{Actual cost} = 1.80 \times 6.6 = 11.88
\]
Now, let's compare this cost to the amount of money Luis has ($12):
- Actual cost of apples: $11.88
- Amount Luis has: $12
Now, estimating the cost by rounding each value might look like this:
- Rounding 6.6 pounds to 7 pounds,
- Rounding the cost of apples per pound from $1.80 to $2.00.
So, using these rounded values:
\[
\text{Estimated cost} = 2.00 \times 7 = 14.00
\]
Now, let's analyze the options:
1. **If each value rounds up**, both the pounds and the price per pound becomes larger, resulting in an estimate that is higher (as we saw, $14.00 compared to the actual $11.88).
2. Since $14.00 (estimated cost) is greater than $12 (Luis's total amount), it means **Luis does not have enough money to buy the apples** based on the rounded estimate.
Thus, the reasoning supports that:
**"Because each value rounds up, his estimate is higher than the actual product. He does not have enough money to buy the apples."**
So the correct answer is the second option:
**Because each value rounds up, his estimate is higher than the actual product. He does not have enough money to buy the apples.**
The cost of apples is $1.80 per pound, and he wants to buy 6.6 pounds:
\[
\text{Actual cost} = 1.80 \times 6.6 = 11.88
\]
Now, let's compare this cost to the amount of money Luis has ($12):
- Actual cost of apples: $11.88
- Amount Luis has: $12
Now, estimating the cost by rounding each value might look like this:
- Rounding 6.6 pounds to 7 pounds,
- Rounding the cost of apples per pound from $1.80 to $2.00.
So, using these rounded values:
\[
\text{Estimated cost} = 2.00 \times 7 = 14.00
\]
Now, let's analyze the options:
1. **If each value rounds up**, both the pounds and the price per pound becomes larger, resulting in an estimate that is higher (as we saw, $14.00 compared to the actual $11.88).
2. Since $14.00 (estimated cost) is greater than $12 (Luis's total amount), it means **Luis does not have enough money to buy the apples** based on the rounded estimate.
Thus, the reasoning supports that:
**"Because each value rounds up, his estimate is higher than the actual product. He does not have enough money to buy the apples."**
So the correct answer is the second option:
**Because each value rounds up, his estimate is higher than the actual product. He does not have enough money to buy the apples.**