A jeweler has 5 rings, each weighing 16 g, made of an alloy of 5% silver and 95% gold.

Question

She decides to melt down the rings and add enough silver to reduce the gold content to 80%. How much silver should she add?

I got 15g. Is that correct?

Answer 1

Hi Danny L.,

We can agree that the 5 rings total 80 g of alloy, with .05(80) = 4 g of silver and 80 - 4 = 76 g gold. But since were asked about silver lets stay with silver and not worry about the gold.

If I may rephrase the question, were asked; How much of a 5% of 80 g silver alloy plus an additional amount of silver will equal a 20% of total grams silver alloy (an 80% gold alloy is a 20% silver alloy in this case). Lets try to write an equation for this:

.05(80 g) silver + x g silver = .20(80 g + x g) silver.

.05(80) + x = .20(80 + x) can you take it from here?

I hope this helps, Joe.

Answer 2

Yes you are correct!!!

First there are a total of 80 grams: 4 g of silver and 76 g of gold

Adding 15 g of silver results in

96 grams: 19 g of silver and 76 grams of gold which have percentages 20% and 80%

The solution is found as follows:

X grams of silver is added to the original 80 grams mixture.

Then the percent silver is (x+4)/(x+80) = 0.2

x+4 = 0.2(x+ 80)

x + 4 = 0.2x + 16

0.8x + 4 = 16

0.8x = 12

8x = 120

x = 15