Expert: Sherry Wallin - 9/6/2009

Question
Sam has been saving 10 cent coins and 20 cent coins in a jar. When he takes the jar to the bank, he finds that there are 252 coins worth a total of $43.20. How many of each coin are there?

Answer
Hi Heba~
    We don't have any 20 cent coins here in the U.S., do you in Australia? Let's pretend that there is such a coin. You have two unknowns and 2 equations. Let x = # of 10 cent coins and y = # of 20 cent coins. You have a total of 252 coins so x+y = 252. Furthermore 10 cent coins are worth .1 of a dollar and 20 cent coins are worth .2 of a dollar so you have .1x + .2y = 43.20. Now solve this system of equations. I would take the 2nd equation and multiply it by 10 to get whole numbers of coins: x + 2y = 432. Solve for x getting
x = 432 - 2y. Put that new value of x into the other equation x + y = 252: 432 - 2y + y = 252 or
432 - y = 252 or y = 180. Now that you know you have 180 20 cent coins you can see that you have 72 qo cent coins either by inspection or by substituting back into either of the other equations:
x + 180 = 252 so x = 252 -180 or x = 72.

Math Prof