Nima uses 2/3 cup peanuts, 1/2 cup cashews, 3/4 cups pecans, and some raisinsin a recipe that makes 2 1/4 cups of trail mix. How many cups of peanuts are there per cup of trail mix?

8/27 cups

Step-by-step explanation:

Nima uses 2/3 cups of peanuts to make a recipe of 2 1/4 = 9/4 cups of trail mix. If we want to find how many cups of peanuts are there per cup of trail mix, we can do a rule of three:

If 9/4 cups of trail mix need 2/3 cups of peanuts, 1 cup of trail mix need X cups of peanuts:

9/4 cups of trail mix - > 2/3 cups of peanuts

1 cup of trail mix - > X cups of peanuts

9/4 / 1 = 2/3 / X

9/4 = 2 / (3*X)

3*X*9 = 4*2

27*X = 8

X = 8/27 cups