Zara bought 2.4 pounds of grapes and a watermelon that cost
7.32. Which describes a way to determine x, the price per pound for the grapes? Divide 7.32 by 2.4 and then subtract 5.28 from the quotient. Subtract 5.28 from 7.32 and then divide the difference by 2.4. Solve for x in the equation 2.4x – 5.28 = 7.32. Solve for x in the equation 2.4 (x + 5.28) = 7.32.
The Correct Answer and Explanation is:
ChatGPT said:
Correct answer:
Subtract 5.28 from 7.32 and then divide the difference by 2.4.
Explanation:
Let’s carefully analyze the problem:
- Zara bought 2.4 pounds of grapes.
- She also bought a watermelon that cost $7.32.
- We want to find x, the price per pound for the grapes.
Step 1: Understanding the total cost
Since Zara bought grapes and a watermelon, the total cost she paid is the sum of the cost of grapes plus the cost of the watermelon.
- Cost of grapes = price per pound × number of pounds = 2.4×x2.4 \times x2.4×x
- Cost of watermelon = $7.32
So, the total amount spent is:Cost of grapes+Cost of watermelon=total cost\text{Cost of grapes} + \text{Cost of watermelon} = \text{total cost}Cost of grapes+Cost of watermelon=total cost
Step 2: The missing piece: What is the total cost?
The problem as stated seems to imply that Zara bought grapes and a watermelon, and somewhere we know the total amount she spent or some related figure involving 5.28. Since it’s not clearly stated, but the options mention 5.28, let’s assume 5.28 is the total amount Zara spent or the amount related to the grapes. Let’s test the options by interpreting 5.28 as the cost of grapes:
- Cost of grapes = 5.28
- Cost of watermelon = 7.32
If this is the case, then Zara spent a total of:5.28+7.32=12.605.28 + 7.32 = 12.605.28+7.32=12.60
Alternatively, if 7.32 is the total Zara spent on grapes and watermelon combined, and 5.28 is the cost of the watermelon or grapes, we can adjust accordingly.
Since the problem states the watermelon costs 7.32, let’s say the total cost of grapes plus watermelon is unknown, but we want to solve for xxx — the price per pound of grapes.
Step 3: Evaluating each given option
- “Divide 7.32 by 2.4 and then subtract 5.28 from the quotient.”
- This means: 7.322.4−5.28\frac{7.32}{2.4} – 5.282.47.32−5.28
- This operation does not represent a logical step for finding the price per pound of grapes because 7.32 is the watermelon price alone, and dividing it by the weight of grapes (2.4) doesn’t relate directly.
- “Subtract 5.28 from 7.32 and then divide the difference by 2.4.”
- This means: 7.32−5.282.4\frac{7.32 – 5.28}{2.4}2.47.32−5.28
- This expression implies: total cost (7.32) minus watermelon cost (5.28) gives the grapes cost, then divide by pounds to get price per pound.
- This makes sense if 7.32 represents the total cost of both items, and 5.28 is the cost of watermelon (or vice versa).
- This method correctly isolates the grape cost, then finds the price per pound.
- “Solve for x in the equation 2.4x – 5.28 = 7.32.”
- Rearranged, this is 2.4x=7.32+5.28=12.62.4x = 7.32 + 5.28 = 12.62.4x=7.32+5.28=12.6, so x=12.62.4=5.25x = \frac{12.6}{2.4} = 5.25x=2.412.6=5.25.
- This means the grapes cost $12.6, which contradicts the given prices (watermelon cost is 7.32).
- This equation mixes costs improperly.
- “Solve for x in the equation 2.4(x + 5.28) = 7.32.”
- This means: 2.4x+2.4×5.28=7.322.4x + 2.4 \times 5.28 = 7.322.4x+2.4×5.28=7.32
- 2.4x+12.672=7.322.4x + 12.672 = 7.322.4x+12.672=7.32
- 2.4x=7.32−12.672=−5.3522.4x = 7.32 – 12.672 = -5.3522.4x=7.32−12.672=−5.352
- x=−2.23x = -2.23x=−2.23 (negative price per pound)
- Negative price is nonsensical, so this is incorrect.
Final conclusion:
The best description that matches a realistic way to find the price per pound of grapes is:Subtract 5.28 from 7.32 and then divide the difference by 2.4.\boxed{ \text{Subtract 5.28 from 7.32 and then divide the difference by 2.4.} }Subtract 5.28 from 7.32 and then divide the difference by 2.4.
This means:
- If 7.32 is the total amount Zara paid for grapes and watermelon combined,
- and 5.28 is the cost of the watermelon,
- then subtracting gives the cost of grapes,
- dividing by the weight of grapes (2.4 pounds) gives the price per pound of grapes.
Summary:
- The cost of grapes = total cost – watermelon cost = 7.32−5.287.32 – 5.287.32−5.28.
- Price per pound of grapes x=cost of grapesweight=7.32−5.282.4x = \frac{\text{cost of grapes}}{\text{weight}} = \frac{7.32 – 5.28}{2.4}x=weightcost of grapes=2.47.32−5.28.
This approach aligns with common word problem-solving techniques where you isolate the unknown cost and then divide by quantity to find the unit price.
