To find out how many pounds of walnuts and raisins are needed to make a 20-pound bag of mix that costs $3.75 per pound, you can set up a system of equations based on the cost and weight of each ingredient.
Let W represent the pounds of walnuts and R represent the pounds of raisins.
You want to create a 20-pound mix, so:
W + R = 20 (equation 1)
You also want the cost of the mix to be $3.75 per pound, which means:
6.25W + 2.50R = 3.75(20) (equation 2)
Now, you can solve this system of equations. Let's start with equation 1:
W + R = 20
Now, isolate W:
W = 20 - R
Next, substitute this expression for W into equation 2:
6.25(20 - R) + 2.50R = 75
Now, distribute and simplify:
125 - 6.25R + 2.50R = 75
Combine like terms:
-3.75R = -50
Now, divide both sides by -3.75 to solve for R:
R = -50 / -3.75
R = 50 / 3.75
R = 13.33... (approximately)
So, you need approximately 13.33 pounds of raisins. Now, use equation 1 to find the amount of walnuts:
W + R = 20
W + 13.33 = 20
W = 20 - 13.33
W = 6.67 pounds
You need approximately 6.67 pounds of walnuts.
Keep in mind that these are approximate values, as it's difficult to have a fraction of a pound of an ingredient. In practical terms, you would likely round these to the nearest whole pound, which would mean approximately 13 pounds of raisins and 7 pounds of walnuts to make the 20-pound bag of mix.