A 25% silver alloy is to be melted with a 55% silver alloy. How many grams of each must be used to obtain 30 grams of a 32% silver alloy?

Let x = grams of 25% silver alloy Let y = grams of 55% silver alloy

We set up 2 equations based on the given information

x + y = 30

.25x + .55y = .32(30) = 9.6

but y = 30 - x so we can substitute

.25x + .55(30-x) = 9.6

.25x + 16.5 - .55x = 9.6

-0.30x = -6.9

x = -6.9/-0.30 = 23 grams

y = 30 -23 = 7 grams

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