weight of gold and silver

[semidevil]

A ten-gram piece of a certain alloy contains only gold and silver. If the piece currently contains exactly 3 grams of silver, how many more grams of gold must be added to the piece so that the resulting piece is 10 percent silver?

oa: 20.

Intuition can tell you the answer fairly quick. 3g of silver of 10-gram alloy is 30%. to get 3%, simple add enough gold that that you get 30-grams of alloy. 3% silver / 30-gram alloy is now 10%.

but what if I was not able to recognize this shortcut. How would one go about algebraically solving this?

[kapsii]

Putting your intuition into algebraic equations:

In the new alloy:
3gms of Silver = 10% of the alloy's weight.
Xgms of gold = 90% of the alloy's weight.

hence X gms should equal (9 * 3) gms or 27 grams.

In the older alloy of 10gms we already have (10 - 3)gms of gold.
i.e. 7 gms.

So, we require additional (27 - 7) gms of gold...

HTH