Question

A trail mix manufacturer makes an organic mix using a specific ratio of mixed nuts, which costs $10.25 per pound, and dried fruit mix, which costs $3.35 per pound. The finished trail mix ends up costing $6.80 per pound. If the manufacturer has 81 pounds of mixed nuts, how many pounds of dried fruit will be needed to make the mix?

A. 12 pounds
B. 16 pounds
C. 18 pounds
D. 20 pounds

Answer 1

Approximately 80.65 pounds of dried fruit will be needed to make the mix, according to the given ratios and prices.

Step-by-step explanation:

To find the amount of dried fruit needed, we can set up a ratio using the prices of the mixed nuts and dried fruit. Let's call the weight of dried fruit needed x. The cost of the mixed nuts is $10.25 per pound, and the cost of the dried fruit is $3.35 per pound. The finished trail mix costs $6.80 per pound. We can set up the following equation:

(81 pounds of mixed nuts) / ($10.25 per pound) + (x pounds of dried fruit) / ($3.35 per pound) = (81 pounds + x pounds) / ($6.80 per pound)

To solve for x, we can cross multiply and solve for x:

(81 * $6.80) + ($3.35 * x) = ($10.25 * 81) + ($6.80 * x)

Simplifying the equation:

551.8 + $3.35x = 830.25 + $6.80x

Subtracting $3.35x and 551.8 from both sides:

$6.80x - $3.35x = 278.45

Combining like terms:

$3.45x = 278.45

Dividing both sides by $3.45:

x = 80.65

So, approximately 80.65 pounds of dried fruit will be needed to make the mix.