Final answer:
By setting up and solving a system of linear equations, we find that walnuts cost $3.50 per pound and chocolate chips cost $1.25 per pound.
Step-by-step explanation:
The question involves using a system of two linear equations to find the cost per pound of walnuts and chocolate chips. We can define w to be the cost of one pound of walnuts and c to be the cost of one pound of chocolate chips. From the information given, we can set up the following two equations:
3w + 2c = 13
8w + 4c = 33
To solve these equations, we can use either substitution or elimination. Let's use elimination:
Multiply the first equation by 2 to align the coefficients of c. This gives us: 6w + 4c = 26.
Now, subtract the newly obtained equation from the second one: (8w + 4c) - (6w + 4c) = 33 - 26, which simplifies to 2w = 7.
Divide both sides by 2 to find w: w = 7/2, so w = $3.50 per pound for walnuts.
Substitute the value of w back into the first equation: 3(3.50) + 2c = 13. Therefore, 10.50 + 2c = 13.
Subtract 10.50 from both sides to find c: 2c = 2.50.
Divide both sides by 2 to get: c = 2.50 / 2, so c = $1.25 per pound for chocolate chips.
Therefore, walnuts cost $3.50 per pound and chocolate chips cost $1.25 per pound.