Math Concentration

Joe has a ring weighing 10 grams made of an alloy of 13% silver and the rest gold. He decides to melt down the rings and add enough silver to reduce the gold content to 69%. How many grams of silver should he add?

My set up is:

10 (.13 + .87) = 10 (.13 + X + .69)

I'm not sure if that's correct.

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  1. Silver = 0.13 * 10 = 1.3 grams.

    Gold = 10 1.3 = 8.7 grams.

    New Alloy: Gold=69% of total solution.

    G / (G+S) = 0.69,
    8.7 / (8.7 + S) = 0.69,
    Cross multiply:
    6 + 0.69S = 8.7,
    0.69S = 8.7 - 6 = 2.7,
    S = 3.91 Grams of silver, total.
    3.91 - 1.3 = 2.6 grams of silver added.

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