Question

select the correct answer. wren is at the grocery store buying fruit. she buys x pounds of apples for $1.68 per pound. she buys 2 fewer pounds of grapes for $2.48 per pound. the cost of the fruit, before tax, is $13.76. how many pounds of each fruit is she buying? a. 2.8 pounds of apples and 4.8 pounds of grapes b. 3.3 pounds of apples and 1.3 pounds of grapes c. 3.8 pounds of apples and 1.8 pounds of grapes d. 4.5 pounds of apples and 2.5 pounds of grapes

Explanation:

Step1: Define variables and equation

Let \( x \) be pounds of apples, grapes are \( x - 2 \) pounds. Cost equation: \( 1.68x + 2.48(x - 2) = 13.76 \).

Step2: Expand and simplify

Expand: \( 1.68x + 2.48x - 4.96 = 13.76 \). Combine like terms: \( 4.16x - 4.96 = 13.76 \).

Step3: Solve for \( x \)

Add 4.96: \( 4.16x = 13.76 + 4.96 = 18.72 \). Divide: \( x = \frac{18.72}{4.16} = 4.5 \)? Wait, no, wait—wait, maybe test options. Let's test option C: Apples 3.8, grapes 1.8 (3.8 - 2 = 1.8). Cost: \( 1.68×3.8 + 2.48×1.8 \). Calculate 1.68×3.8 = 6.384, 2.48×1.8 = 4.464. Sum: 6.384 + 4.464 = 10.848 ≠13.76. Wait, maybe I made a mistake. Wait, let's test option D: 4.5 apples, 2.5 grapes (4.5 - 2 = 2.5). Cost: 1.68×4.5 = 7.56, 2.48×2.5 = 6.2. Sum: 7.56 + 6.2 = 13.76. Wait, but 4.5 - 2 = 2.5, which matches. But wait, the options: Wait, option C is 3.8 and 1.8 (3.8-2=1.8), option D is 4.5 and 2.5 (4.5-2=2.5). Wait, let's recalculate the equation. Original equation: \( 1.68x + 2.48(x - 2) = 13.76 \). Let's solve it properly. Expand: 1.68x + 2.48x - 4.96 = 13.76. Combine: 4.16x = 13.76 + 4.96 = 18.72. x = 18.72 / 4.16 = 4.5. So x=4.5, so apples 4.5, grapes 2.5. But wait, the options: Option D is 4.5 apples and 2.5 grapes. But wait, let's check the options again. Wait, maybe I miscalculated earlier. Wait, option D: 4.5 and 2.5. 4.5 - 2 = 2.5, correct. Cost: 4.5×1.68 = 7.56, 2.5×2.48 = 6.2. 7.56 + 6.2 = 13.76. Correct. But wait, the options: Wait, maybe I misread the options. Wait, the options: A: 2.8 and 4.8 (2.8-2=0.8≠4.8). B: 3.3 and 1.3 (3.3-2=1.3). Cost: 1.68×3.3=5.544, 2.48×1.3=3.224. Sum: 5.544+3.224=8.768≠13.76. C: 3.8 and 1.8: 1.68×3.8=6.384, 2.48×1.8=4.464. Sum=10.848≠13.76. D: 4.5 and 2.5: 1.68×4.5=7.56, 2.48×2.5=6.2. Sum=13.76. Wait, but 4.5-2=2.5, which is correct. But wait, the problem says "2 fewer pounds of grapes", so grapes are x-2, so if apples are x, grapes are x-2. So x=4.5, grapes=2.5. So option D? Wait, but let's check the options again. Wait, the options: A: 2.8 and 4.8 (2.8-2=0.8≠4.8, so invalid). B: 3.3 and 1.3 (3.3-2=1.3, valid). Cost: 1.68×3.3=5.544, 2.48×1.3=3.224. Sum=8.768≠13.76. C: 3.8 and 1.8 (3.8-2=1.8, valid). Cost: 1.68×3.8=6.384, 2.48×1.8=4.464. Sum=10.848≠13.76. D: 4.5 and 2.5 (4.5-2=2.5, valid). Cost: 1.68×4.5=7.56, 2.48×2.5=6.2. Sum=13.76. So D is correct? Wait, but the initial equation solving gave x=4.5, which is option D. But wait, maybe I made a mistake in the equation. Wait, the problem says "2 fewer pounds of grapes", so grapes = apples - 2. So if apples is x, grapes is x - 2. So the cost is 1.68x + 2.48(x - 2) = 13.76. Solving: 1.68x + 2.48x - 4.96 = 13.76 → 4.16x = 13.76 + 4.96 = 18.72 → x = 18.72 / 4.16 = 4.5. So apples 4.5, grapes 2.5, which is option D. But wait, the options: D is 4.5 pounds of apples and 2.5 pounds of grapes. So that's correct.

Answer:

D. 4.5 pounds of apples and 2.5 pounds of grapes