Question

How much of a 90% alloy must be combined with 70% gold alloy in order to get 60 ounces of an 85% gold alloy?

Answer 1

x = amount of 90% alloy
y = amount of 70% alloy

x + y = 60
0.9x + 0.7y = 0.85*60

0.9x + 0.7(60 - x) = 0.85*60
(0.9 - 0.7)x = (0.85 - 0.7)*60
x = (0.85 - 0.7)*60/(0.9 - 0.7)
x = 45 ounces

y = 60 - 45
y = 15 ounces

Answer 2

45 ounce a 90% alloy must be combined with 15 ounce of a 70% gold alloy in order to get 60 ounces of an 85% gold alloy.

Let x represent the number of 90% alloy and y represent the number of 70% gold alloy in ounce.

Since 60 ounces of an 85% gold alloy is needed, hence:

x + y = 60     (1)

Also:

90% of x + 70% of y = 85% of 60

0.9x + 0.7y = 51    (2)

Solving equation 1 and 2 simultaneously gives:

x = 45, y = 15

Therefore of 45 ounce a 90% alloy must be combined with 15 ounce of a 70% gold alloy in order to get 60 ounces of an 85% gold alloy.

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