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:
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 $5.28 (implied by the problem context).
- The total cost for grapes and watermelon is $7.32.
- We want to find x, the price per pound for the grapes.
Step 1: Set up the equation
If the grapes cost x dollars per pound, then the total cost for the grapes is:2.4×x2.4 \times x2.4×x
The watermelon cost is given as $5.28.
The total cost for both grapes and watermelon is:2.4x+5.28=7.322.4x + 5.28 = 7.322.4x+5.28=7.32
Step 2: Solve for x
To find the price per pound for the grapes, isolate xxx:2.4x+5.28=7.322.4x + 5.28 = 7.322.4x+5.28=7.32
Subtract 5.28 from both sides:2.4x=7.32−5.282.4x = 7.32 – 5.282.4x=7.32−5.28
Calculate the difference:2.4x=2.042.4x = 2.042.4x=2.04
Now, divide both sides by 2.4:x=2.042.4x = \frac{2.04}{2.4}x=2.42.04
Step 3: Interpret the problem choices
- “Divide 7.32 by 2.4 and then subtract 5.28 from the quotient” This would be: 7.322.4−5.28\frac{7.32}{2.4} – 5.282.47.32−5.28 This is incorrect because the watermelon cost is a fixed amount and should be subtracted before dividing.
- “Subtract 5.28 from 7.32 and then divide the difference by 2.4” This is: 7.32−5.282.4\frac{7.32 – 5.28}{2.4}2.47.32−5.28 This matches the algebraic steps we performed and is the correct way to find the price per pound.
- “Solve for x in the equation 2.4x−5.28=7.322.4x – 5.28 = 7.322.4x−5.28=7.32” This rearranges the watermelon cost incorrectly with a minus sign instead of plus. This equation does not fit the problem since costs add up.
- “Solve for x in the equation 2.4(x+5.28)=7.322.4 (x + 5.28) = 7.322.4(x+5.28)=7.32” This means the price per pound of grapes is x+5.28x + 5.28x+5.28, which inflates the price of grapes incorrectly. This is not correct.
Summary:
The watermelon cost is a fixed $5.28, and the total is $7.32. The grapes cost per pound times 2.4 pounds plus 5.28 equals 7.32. To isolate the grapes price per pound, subtract the watermelon cost from the total first, then divide by the pounds of grapes.
Therefore, the correct method is:
Subtract 5.28 from 7.32 and then divide the difference by 2.4.
