Question

Taylor sells trail mix consisting of nuts and raisins for $6.60 per pound. The nuts cost $8 per pound and the raisins cost $4.50 per pound. She has 10 pounds of raisins and wants to make 25 pounds of trail mix. How many pounds of nuts should she mix with the 10 pounds of raisins so that she breaks even, neither gains nor loses money selling the trail mix? Write and solve an equation to justify your answer. State your answer in a complete sentence.

Answer 1

Let's represent the pounds of nuts as "x". The cost of the nuts would be 8x dollars, and the cost of the raisins is 10 * 4.50 = 45 dollars. The total cost of making the trail mix is the sum of these two costs.

Total cost = Cost of nuts + Cost of raisins
Total cost = 8x + 45

Since Taylor wants to make 25 pounds of trail mix, the selling price should cover the total cost to break even:

Selling price = Total cost
6.60 * 25 = 8x + 45

165 = 8x + 45

Now, solve for x:

8x = 165 - 45
8x = 120
x = 15

Taylor should mix 15 pounds of nuts with the 10 pounds of raisins to break even.