The Correct Answer and Explanation is:
The correct answer is: (3 + 0.9) × 1 + (3 + 0.9) × 0.80.
To solve this problem, we must find the total cost of 3.9 pounds of grapes priced at $1.80 per pound. The simplest approach is to multiply 3.9 by 1.80 directly, which gives the total cost. However, since the question provides answer choices that deconstruct the price into dollars and cents, we must interpret the expression accordingly.
The cost per pound is $1.80, which is equivalent to 1 dollar and 80 cents. Also, the weight is 3.9 pounds, which can be written as 3 pounds plus 0.9 pounds.
Now let us evaluate the expression (3 + 0.9) × 1 + (3 + 0.9) × 0.80:
- First, calculate (3 + 0.9), which equals 3.9.
- Multiply this 3.9 by 1 to get the dollar portion: 3.9 × 1 = 3.9 dollars.
- Then multiply 3.9 by 0.80 to get the cents portion in dollar form: 3.9 × 0.80 = 3.12 dollars.
- Add both results: 3.9 + 3.12 = 7.02 dollars.
This matches the total cost of 3.9 pounds at $1.80 per pound (3.9 × 1.80 = 7.02).
The other choices involve incorrect mathematical operations or reinterpret the values in ways that no longer represent the unit price or the proper total weight. For example, (3 × 0.9) × 1 does not accurately describe the total weight, and (3 – 0.9) represents a subtraction that conflicts with the known quantity.
Therefore, the most accurate expression is the one that splits 3.9 into 3 and 0.9, then multiplies each component by 1 and 0.80 respectively, reflecting the dollar and cent components of the price.
