Final answer:
To determine the number of bags of each mix the Math Team should make, set up a proportion using the ratios of fruit to nuts. Solve the proportion to find the number of cups of fruit in the crunchy mix. Subtract from 30 to find the number of cups of fruit in the fruity mix.
Step-by-step explanation:
To determine how many bags of each mix the Math Team should make, we need to find the ratio of fruit to nuts in each mix and the total cups of each ingredient available. The ratio of fruit to nuts for the crunchy mix is 5:50, which simplifies to 1:10. The ratio for the fruity mix is 7:30, which simplifies to 7:30. Based on these ratios, we can set up the following proportion:
x/10 = (30- x)/30
Where x represents the number of cups of fruit in the crunchy mix. We can solve this proportion to find the value of x, which will give us the number of cups of fruit in the crunchy mix. Then, we can subtract x from 30 to find the number of cups of fruit in the fruity mix.