Final answer:
To find out how many pounds of raisins and walnuts Diego bought, we can set up a system of equations representing the cost and quantity of the ingredients. By solving this system, we can determine that Diego bought 1/4 pound of raisins and 1 3/4 pounds of walnuts.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's say Diego bought x pounds of raisins and y pounds of walnuts. The cost of the raisins would be 4x dollars and the cost of the walnuts would be 8y dollars. We know that the total cost of both ingredients is 15 dollars, so we can write the equation 4x + 8y = 15. We also know that Diego bought a total of 2 pounds, so we can write the equation x + y = 2. Now we can solve this system of equations using substitution or elimination.
Multiplying the second equation by 4, we get 4x + 4y = 8. Subtracting this equation from the first equation, we get 4x + 8y - (4x + 4y) = 15 - 8. Simplifying this, we get 4y = 7, which means y = 7/4. Plugging this value into the second equation, we can solve for x: x + 7/4 = 2. Subtracting 7/4 from both sides, we get x = 8/4 - 7/4, which simplifies to x = 1/4. Therefore, Diego bought 1/4 pound of raisins and 7/4 pound (or 1 3/4 pounds) of walnuts.