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?
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?
