He held his fifty-six dollars clutched in a crumpled ball in my pocket.
Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?
To solve his puzzle, you need to use the total number of coins, the values of the two types of coines, and the total value of those coins.
There are twenty-six coins in total. Some of them are quarter coins; let "q" stand for the number of quarters. The rest of the coins are dollar coins. Since there are 26 coins in total and q of them are quarter coins, then there are 26 – q coins left to be dollar coins.
If your uncle has only one quarter, then 25×1 = 25 cents comes from quarters. If he has two quarters, then 25×2 = 50 cents comes from quarters. Since he has q quarters, then 25×q = 25q cents comes from quarters.
For the dollar coins, we need first to convert their value to cents; one dollar is one hundred cents. Since he has 26 – q dollars, then he has 100(26 – q) cents from the dollar coins.
He has seventeen dollars in total, or 1700 cents, part of which is from quarters and part of which is from dollars. To help keep things straight, we can set up a table: