Question
Katherine bought 3 ½ pounds of oranges for $1.45 per pound, as well as 4 ¾ pounds of potatoes that cost $1.69 for 2 pounds. She gives the cashier a $10.00 bill.
Which equation represents the situation if x is the amount of change in dollars Katherine should receive?
Responses
3 ½ (1.45)+4 ¾ (1.692)−x=10
3 ½ (1.45)+4 ¾ (1.69)+x=10
(3 ½ +4 ¾ )⋅(1.45+1.69)+x=10
3 ½ (1.45)+ 4 ¾ (1.64/2 )+=10
Which equation represents the situation if x is the amount of change in dollars Katherine should receive?
Responses
3 ½ (1.45)+4 ¾ (1.692)−x=10
3 ½ (1.45)+4 ¾ (1.69)+x=10
(3 ½ +4 ¾ )⋅(1.45+1.69)+x=10
3 ½ (1.45)+ 4 ¾ (1.64/2 )+=10
Answers
GPT-4o mini
To determine the correct equation representing the situation described, we need to calculate the total cost of the oranges and potatoes, and then relate that to the $10.00 bill with the amount of change (x) Katherine should receive.
1. **Cost of oranges**: Katherine bought \(3 \frac{1}{2}\) pounds of oranges at $1.45 per pound.
\[
\text{Cost of oranges} = 3.5 \times 1.45
\]
2. **Cost of potatoes**: She bought \(4 \frac{3}{4}\) pounds of potatoes that cost $1.69 for every 2 pounds.
First, we need to find the cost per pound:
\[
\text{Cost per pound for potatoes} = \frac{1.69}{2} = 0.845
\]
Then, calculate the cost:
\[
\text{Cost of potatoes} = 4.75 \times 0.845
\]
3. **Total cost** of both items:
\[
\text{Total cost} = (3.5 \times 1.45) + (4.75 \times 0.845)
\]
4. **Change received**: Given that Katherine pays with a $10.00 bill, we can express the situation with the equation:
\[
10 - \text{Total cost} = x
\]
Rearranging gives us:
\[
\text{Total cost} + x = 10
\]
Now let's look at the available options:
- **Option 1**: \( 3 \frac{1}{2} (1.45) + 4 \frac{3}{4} (1.692) - x = 10 \) (Incorrect format, also uses incorrect cost per pound for potatoes)
- **Option 2**: \( 3 \frac{1}{2} (1.45) + 4 \frac{3}{4} (1.69) + x = 10 \) (This captures the relationship but adds instead of subtracting)
- **Option 3**: \( (3 \frac{1}{2} + 4 \frac{3}{4}) \cdot (1.45 + 1.69) + x = 10 \) (Incorrect, since it combines weights inappropriately)
- **Option 4**: \( 3 \frac{1}{2} (1.45) + 4 \frac{3}{4} (1.64 / 2) + x = 10 \) (This uses more incorrect values)
Since none of the statements match the correct arrangement derived, the second equation is the closest to being correct but should be rearranged.
**Correct Equation (from analysis)**:
\[
3.5(1.45) + 4.75 \left(\frac{1.69}{2}\right) + x = 10
\]
However, it's actually better represented as:
\[
3.5(1.45) + 4.75(0.845) + x = 10
\]
If we need to pick the most appropriately structured statement based on the information given, **the closest one is the second option**. But do note that it needs to be rearranged or adjusted based on expressions provided above to be fully accurate:
*Final Answer*: \( \text{no option precisely matches, but Option 2 is closest and can be modified for accuracy.} \)
1. **Cost of oranges**: Katherine bought \(3 \frac{1}{2}\) pounds of oranges at $1.45 per pound.
\[
\text{Cost of oranges} = 3.5 \times 1.45
\]
2. **Cost of potatoes**: She bought \(4 \frac{3}{4}\) pounds of potatoes that cost $1.69 for every 2 pounds.
First, we need to find the cost per pound:
\[
\text{Cost per pound for potatoes} = \frac{1.69}{2} = 0.845
\]
Then, calculate the cost:
\[
\text{Cost of potatoes} = 4.75 \times 0.845
\]
3. **Total cost** of both items:
\[
\text{Total cost} = (3.5 \times 1.45) + (4.75 \times 0.845)
\]
4. **Change received**: Given that Katherine pays with a $10.00 bill, we can express the situation with the equation:
\[
10 - \text{Total cost} = x
\]
Rearranging gives us:
\[
\text{Total cost} + x = 10
\]
Now let's look at the available options:
- **Option 1**: \( 3 \frac{1}{2} (1.45) + 4 \frac{3}{4} (1.692) - x = 10 \) (Incorrect format, also uses incorrect cost per pound for potatoes)
- **Option 2**: \( 3 \frac{1}{2} (1.45) + 4 \frac{3}{4} (1.69) + x = 10 \) (This captures the relationship but adds instead of subtracting)
- **Option 3**: \( (3 \frac{1}{2} + 4 \frac{3}{4}) \cdot (1.45 + 1.69) + x = 10 \) (Incorrect, since it combines weights inappropriately)
- **Option 4**: \( 3 \frac{1}{2} (1.45) + 4 \frac{3}{4} (1.64 / 2) + x = 10 \) (This uses more incorrect values)
Since none of the statements match the correct arrangement derived, the second equation is the closest to being correct but should be rearranged.
**Correct Equation (from analysis)**:
\[
3.5(1.45) + 4.75 \left(\frac{1.69}{2}\right) + x = 10
\]
However, it's actually better represented as:
\[
3.5(1.45) + 4.75(0.845) + x = 10
\]
If we need to pick the most appropriately structured statement based on the information given, **the closest one is the second option**. But do note that it needs to be rearranged or adjusted based on expressions provided above to be fully accurate:
*Final Answer*: \( \text{no option precisely matches, but Option 2 is closest and can be modified for accuracy.} \)