Question

1. diego bought some raisins and walnuts to make trail mix. raisins cost $4 a pound and walnuts cost $8 a pound. diego spent $15 on both ingredients. diego bought a total of 2 pounds of raisins and walnuts. what is the price for each pound of raisins and walnuts?

Explanation:

Step1: Define variables

Let \( x \) be the pounds of raisins and \( y \) be the pounds of walnuts. We know two equations: \( x + y = 2 \) (total pounds) and \( 4x + 8y = 15 \) (total cost).

Step2: Solve the system of equations

From \( x + y = 2 \), we get \( x = 2 - y \). Substitute into the cost equation: \( 4(2 - y)+8y = 15 \).

Step3: Simplify the equation

Expand: \( 8 - 4y + 8y = 15 \), which becomes \( 8 + 4y = 15 \).

Step4: Solve for y

Subtract 8: \( 4y = 15 - 8 = 7 \), so \( y=\frac{7}{4} = 1.75 \). Then \( x = 2 - 1.75 = 0.25 \). But wait, the question asks for the price per pound, which is given as raisins \$4 per pound and walnuts \$8 per pound. Maybe a mis - question, but if we check the cost: \( 4\times0.25+8\times1.75 = 1 + 14 = 15 \), which matches. So the price per pound of raisins is \$4 and walnuts is \$8.

Answer:

The price per pound of raisins is \$4 and the price per pound of walnuts is \$8.