Final answer:
The store needs 8 pounds each of the $6 trail mix (type 1) and the $5 trail mix (type 2) to make a 16-pound mixture selling for $5.50 per pound. This is found by setting up simultaneous equations based on the prices and total weight.
Step-by-step explanation:
Calculating the Trail Mix Combination
To solve this problem, we need to set up an equation based on the given prices of the two types of trail mix and the desired price of the mixture. Let's denote the pounds of the $6 trail mix as x and the pounds of the $5 trail mix as y. The total weight of the mixture is given as 16 pounds, so we can write our first equation as x + y = 16.
Next, we calculate the cost of each type of trail mix in the mixture. We want the overall mixture to sell for $5.50 per pound, so the total cost of the mixture will be 16 pounds times $5.50, which equals $88. Now we can set up our second equation based on the cost: 6x + 5y = 88.
Solving these two equations simultaneously, we multiply the first equation by 5 to eliminate y and get 5x + 5y = 80. Subtract this from the second equation to find the value of x: (6x + 5y) - (5x + 5y) = 88 - 80, which simplifies to x = 8. Using the value of x in the first equation, we find y: 8 + y = 16, so y = 8.
Therefore, the store needs 8 pounds of type 1 mix and 8 pounds of type 2 mix to create a 16-pound mixture that sells for $5.50 a pound, which corresponds to option b).