Write system of equations and solve using any method (graphing, substitution, or elimination)

Question

The drama club sells hot chocolate and coffee at the school´s football games to raise money. At one game they sold $200 worth of hot drinks. If they used 295 cups that night, and they sold hot chocolate for 75 cents and coffee for 50 cents, how many of each drink did they sell?

Answer 1

H=cups of hot chocolate, C=cups of coffee

H+C=295

.75H+.5C=200

Multiply the top equation by 75 and the bottom equation by 100.

Then subtract to eliminate H and solve for C.

Answer 2

Let h be the number of hot chocolates and c be the number of coffees.

h + c = 295

.75h +.50c = 200

If we double the second equation and subtract the first equation to eliminate c,

1.5h + c = 400

-h - c = -295

--------------------

.5h = 105

h=210 hot chocolates

c = 295 -210 = 85 coffees