A cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8

A cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8 1/4 cups, how much flour and how much sugar would it be?

Let f be the number of cups of sugar. And let f be the number of cups of flour. We're given two equations:

1. f = 10s
2. s + f = 8 & 1/4

Substitute (1) into (2):
s + 10s = 8 & 1/4
11fs= 33/4 <-- 8 & 1/4 = 33/4

Cross multiply:
44s = 33

Divide each side by 44:
s= 33/44

Divide top and bottom by 11 and we get s = 3/4 or 0.75

Now substitute this into (1):
f = 10(33/44)
f = 330/44 or 7 & 22/44 or 7.5