Question
Nico paid $15.32 for 4.3 pounds of blueberries. Nico estimated the cost per pound to be $5.00. Which statement explains Nico’s error?
Nico rounded $15.32 to $15.00 and 4.3 pounds to 6 before dividing.
Nico rounded $15.32 to $15.00 and 4.3 pounds to 3 before dividing.
Nico rounded $15.32 to $16.00 and 4.3 pounds to 4 before dividing.
Nico rounded $15.32 to $10.00 and 4.2 pounds to 2 before dividing.
Nico rounded $15.32 to $15.00 and 4.3 pounds to 6 before dividing.
Nico rounded $15.32 to $15.00 and 4.3 pounds to 3 before dividing.
Nico rounded $15.32 to $16.00 and 4.3 pounds to 4 before dividing.
Nico rounded $15.32 to $10.00 and 4.2 pounds to 2 before dividing.
Answers
GPT-4o mini
To determine which statement explains Nico’s error in estimating the cost per pound of blueberries, we can analyze how he might have arrived at the erroneous estimate of $5.00 per pound.
1. The actual cost per pound is calculated by dividing the total cost by the total weight:
\[
\text{Cost per pound} = \frac{\text{Total Cost}}{\text{Total Weight}} = \frac{15.32}{4.3}
\]
Now, calculate the exact figure:
\[
\text{Cost per pound} = \frac{15.32}{4.3} \approx 3.56
\]
2. Nico estimated the cost per pound to be $5.00. This means that in his calculations, he must have arrived at a larger pound value, or a significantly smaller cost.
Now, let’s analyze the statements:
- **Option 1:** "Nico rounded $15.32 to $15.00 and 4.3 pounds to 6 before dividing."
- This would give:
\[
\frac{15.00}{6} = 2.50
\]
- which is incorrect but not $5.00.
- **Option 2:** "Nico rounded $15.32 to $15.00 and 4.3 pounds to 3 before dividing."
- This would give:
\[
\frac{15.00}{3} = 5.00
\]
- This matches his erroneous estimate.
- **Option 3:** "Nico rounded $15.32 to $16.00 and 4.3 pounds to 4 before dividing."
- This would give:
\[
\frac{16.00}{4} = 4.00
\]
- which does not result in a $5.00 estimate.
- **Option 4:** "Nico rounded $15.32 to $10.00 and 4.2 pounds to 2 before dividing."
- This would give:
\[
\frac{10.00}{2} = 5.00
\]
- This also results in a $5.00 estimate, but he did not round the weight to 2 pounds correctly.
Thus, the correct explanation for Nico's error is:
**Nico rounded $15.32 to $15.00 and 4.3 pounds to 3 before dividing.**
1. The actual cost per pound is calculated by dividing the total cost by the total weight:
\[
\text{Cost per pound} = \frac{\text{Total Cost}}{\text{Total Weight}} = \frac{15.32}{4.3}
\]
Now, calculate the exact figure:
\[
\text{Cost per pound} = \frac{15.32}{4.3} \approx 3.56
\]
2. Nico estimated the cost per pound to be $5.00. This means that in his calculations, he must have arrived at a larger pound value, or a significantly smaller cost.
Now, let’s analyze the statements:
- **Option 1:** "Nico rounded $15.32 to $15.00 and 4.3 pounds to 6 before dividing."
- This would give:
\[
\frac{15.00}{6} = 2.50
\]
- which is incorrect but not $5.00.
- **Option 2:** "Nico rounded $15.32 to $15.00 and 4.3 pounds to 3 before dividing."
- This would give:
\[
\frac{15.00}{3} = 5.00
\]
- This matches his erroneous estimate.
- **Option 3:** "Nico rounded $15.32 to $16.00 and 4.3 pounds to 4 before dividing."
- This would give:
\[
\frac{16.00}{4} = 4.00
\]
- which does not result in a $5.00 estimate.
- **Option 4:** "Nico rounded $15.32 to $10.00 and 4.2 pounds to 2 before dividing."
- This would give:
\[
\frac{10.00}{2} = 5.00
\]
- This also results in a $5.00 estimate, but he did not round the weight to 2 pounds correctly.
Thus, the correct explanation for Nico's error is:
**Nico rounded $15.32 to $15.00 and 4.3 pounds to 3 before dividing.**