SOLUTION: you have a piggy bank containing a total of
90 coins in dimes and quarters. If the piggy bank contains $15.45
how many dimes are there in the piggy bank?
Question 1132876: you have a piggy bank containing a total of
90 coins in dimes and quarters. If the piggy bank contains $15.45
how many dimes are there in the piggy bank? Answer by greenestamps(13200) (Show Source):
let x be the number of quarters; then 90-x is the number of dimes. The total value -- 25 cents for each quarter and 10 cents for each dime -- is $15.45, or 1545 cents. So
That equation is easily solved for x, the number of quarters; then the number of dimes is 90-x.
Of course you could save a bit of time by letting x be the number of dimes; then solving the resulting equation would give you the answer to the problem directly.
If an algebraic solution is not required, a bit of logical reasoning and mental arithmetic can solve the problem quickly.
(1) If all 90 coins were dimes, the value would be 900 cents; that is 645 cents less than the actual total.
(2) Exchanging a dime for a quarter keeps the same total of 90 coins but increases the total value by 15 cents (the difference between the value of the quarter and the value of the dime).
(3) To make up the required additional 645 cents, the number of dimes to be replaced by quarters is 645/15 = 43.
So there are 43 quarters in the piggy bank and 90-43 = 47 dimes.
