A goldsmith has two alloys of gold, the first being 70% pure and the second being 60% pure. How many ounces of the 60% pure gold must be used to make 100 ounces of an alloy which will be 66% gold?
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Answer:
Step-by-step explanation:Let X be the amount of 60% pure alloy and Y be the amount of 70% pure alloy.
First, the total weight is
1.X%2BY=100
Next, the percentage of alloy is,
2.0.60%2AY%2B0.70%2AY=0.66%2A%28100%29
Let's use eq. 1 to solve for X in terms of Y,
1.X%2BY=100
X=100-Y
Now substitute that into eq. 2 and solve for y.
2.0.60%2AX%2B0.70%2AY=0.66%2A%28100%29
0.60%2A%28100-Y%29%2B0.70%2AY=0.66%2A%28100%29
60-0.60Y%2B0.70Y=66