If cashews cost $5.00 per pound and peanuts cost $1.50 per pound how do I write the formula to determine how many pound of cashews to mix with 30 pound of peanuts so that the mix will sell for $3.00 per pound.
Let C = weight cashews.
30(1.50) + 5.00*C = (30+C)(3.00)
Let C be the # of pounds of cashews and 30 be the # of pounds of peanuts.
$3 times the total number of lb. equals the sum of the costs of separate purchases of peanuts and cashews.
(C + 30)* 3 = 5 C + 1.50*30 = 5C + 45
Solve for C
To determine the number of pounds of cashews to mix with 30 pounds of peanuts in order to sell the mix for $3.00 per pound, you can use the concept of weighted averages.
Let's denote the number of pounds of cashews needed as x.
To find the weighted average, we need to take into account the price per pound of each ingredient and their respective weights.
The total weight of the peanuts and cashews combined is the sum of their individual weights. In this case, it is 30 pounds + x pounds, or 30 + x pounds.
Now, let's determine the total cost of the mix. The total cost is the sum of the cost of the peanuts (30 pounds multiplied by $1.50 per pound) and the cost of the cashews (x pounds multiplied by $5.00 per pound). It can be represented as:
(30 * 1.50) + (x * 5.00)
Finally, we'll calculate the weighted average by dividing the total cost of the mix by the total weight of the mix. We want the weighted average to be $3.00 per pound, so we can set up the following equation:
((30 * 1.50) + (x * 5.00)) / (30 + x) = 3.00
Simplifying this equation will allow us to solve for x and find the number of pounds of cashews to mix with the peanuts.