Question

Jo makes fruit salad with grapefruit and pineapple. Grapefruit costs $1.25 per 12 oz can, and pineapple costs $0.83 per 12 oz can. How many cans should she mix to obtain 84 oz of a mixture that will sell for $1.01 for 12 oz?

Answer 1

To find out how many cans of grapefruit and pineapple Jo should mix to obtain 84 oz of a mixture that will sell for $1.01 per 12 oz, we need to set up a system of equations. Solving these equations, we find that Jo should mix 7.5 cans of grapefruit and 4.5 cans of pineapple to obtain the desired mixture.

Step-by-step explanation:

To find out how many cans of grapefruit and pineapple Jo should mix to obtain 84 oz of a mixture that will sell for $1.01 per 12 oz, we need to set up a system of equations.

Let's assume Jo mixes x cans of grapefruit and y cans of pineapple. The cost of the grapefruit mix would be 1.25x dollars and the cost of the pineapple mix would be 0.83y dollars.

Since the total volume of the mixture is 84 oz and each can is 12 oz, we can write the equation 12x + 12y = 84.

Also, since the cost of the mixture is $1.01 per 12 oz, we can write the equation 1.25x + 0.83y = 1.01.

Solving these two equations, we can find the values of x and y, which will tell us how many cans of each fruit Jo should mix.

For example, multiplying the first equation by 0.83, we get 9.96x + 9.96y = 69.12. Subtracting this equation from the second equation, we get 4.4x = 33.12. Dividing both sides by 4.4, we find that x = 7.5.

Thus, Jo should mix 7.5 cans of grapefruit and the remaining 84 / 12 - 7.5 = 4.5 cans of pineapple to obtain the desired mixture.