How much 50% gold alloy and 30% gold alloy should be combined to obtain 80 ounces of 45% gold alloy?

Question

Applying the concept

Answer 1

x = amount of 50% gold alloy, in ounces
y = amount of 30% gold alloy, in ounces
80 ounces total of 45% alloy

Set this up as a weighted combination of the alloys:

(0.50)x + (0.30)y = (0.45)(80) = 36
x + y = 80

Solve for x and y.

x = 80 - y
0.50(80 - y) + 0.30y = 36

40 - 0.5y + 0.3y = 36

4 = 0.2y

y = 4/0.2 = 20 ounces of 30% gold alloy

x = 80 - y = 80 - 20 = 60 ounces of 50% gold alloy