Question
Cherries cost $5.68 a pound. Will $20 be enough to buy a 4.1-pound bag of cherries?
Explain how to determine whether $20 is the correct estimate of the product of $5.68(4.1).
Explain how to determine whether $20 is the correct estimate of the product of $5.68(4.1).
Answers
GPT-4o mini
To determine if $20 is enough to buy a 4.1-pound bag of cherries that costs $5.68 per pound, we need to calculate the total cost of the cherries.
First, calculate the total cost using the formula:
\[ \text{Total Cost} = \text{Cost per pound} \times \text{Weight in pounds} \]
Substituting the given values:
\[ \text{Total Cost} = 5.68 \times 4.1 \]
Now, we can estimate the product \( 5.68 \times 4.1 \).
To make the multiplication easier, we can round the numbers:
- Round \( 5.68 \) to \( 5.7 \) (for simplicity, you could also round it down to \( 5.5 \) to get a more conservative estimate).
- Round \( 4.1 \) to \( 4 \).
Now, we perform the estimated multiplication:
\[ 5.7 \times 4 \approx 22.8 \]
If we have rounded \( 5.68 \) down to \( 5.5 \) for a conservative estimate, we would compute:
\[ 5.5 \times 4 \approx 22.0 \]
In either case (using \( 5.7 \) or \( 5.5 \)), the estimated total cost is around \( 22 \) dollars, which exceeds \( 20 \) dollars.
Now, let's more precisely compute the actual multiplication:
You can compute \( 5.68 \times 4.1 \) directly:
1. Break it down:
- \( 5.68 \times 4 = 22.72 \)
- \( 5.68 \times 0.1 = 0.568 \)
2. Add these results:
\[ 22.72 + 0.568 = 23.288 \]
The total cost is approximately \( 23.29 \) dollars, which confirms that \( 20 \) dollars will **not** be sufficient to buy a 4.1-pound bag of cherries at the given price.
### Conclusion:
$20 is not enough to buy a 4.1-pound bag of cherries, as the estimated cost of approximately $23.29 exceeds $20.
First, calculate the total cost using the formula:
\[ \text{Total Cost} = \text{Cost per pound} \times \text{Weight in pounds} \]
Substituting the given values:
\[ \text{Total Cost} = 5.68 \times 4.1 \]
Now, we can estimate the product \( 5.68 \times 4.1 \).
To make the multiplication easier, we can round the numbers:
- Round \( 5.68 \) to \( 5.7 \) (for simplicity, you could also round it down to \( 5.5 \) to get a more conservative estimate).
- Round \( 4.1 \) to \( 4 \).
Now, we perform the estimated multiplication:
\[ 5.7 \times 4 \approx 22.8 \]
If we have rounded \( 5.68 \) down to \( 5.5 \) for a conservative estimate, we would compute:
\[ 5.5 \times 4 \approx 22.0 \]
In either case (using \( 5.7 \) or \( 5.5 \)), the estimated total cost is around \( 22 \) dollars, which exceeds \( 20 \) dollars.
Now, let's more precisely compute the actual multiplication:
You can compute \( 5.68 \times 4.1 \) directly:
1. Break it down:
- \( 5.68 \times 4 = 22.72 \)
- \( 5.68 \times 0.1 = 0.568 \)
2. Add these results:
\[ 22.72 + 0.568 = 23.288 \]
The total cost is approximately \( 23.29 \) dollars, which confirms that \( 20 \) dollars will **not** be sufficient to buy a 4.1-pound bag of cherries at the given price.
### Conclusion:
$20 is not enough to buy a 4.1-pound bag of cherries, as the estimated cost of approximately $23.29 exceeds $20.