12 cups were used so H + F = 12

You sold $8 so .5H + .75F = 8

Solve the first equation in terms of one variable.
H+F=12
F = 12-H | Substitute that into the second equation.
.5H + .75(12-H) = 8
.5H + 9 - .75H = 8
-.25H = -1
H = 4

H+F = 12
4+F=12
F=12-4=8

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Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = number of full cups sold
Let = number of half cups sold
given:
(1)
(2)
---------------
(2)
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)


and, since
(1)
(1)
You sold 4 half cups and 8 full cups