Bofa has a bag of money amounting to $4.32. It contains 108 coins, all of them dimes or pennies. How many pennies are there?
Solution
This can be done b y guess-and-try; you'll get 36 dimes and 72 pennies.
But you can also go by thinking of the extreme cases.
If all 108 coins were pennies, there would be $1.08.
Every time a penny is replaced by a dime, the amount goes up by 9 cents.
So if there are are x dimes, the amount goes up by 0.09x.
So to increase the amount of money from $1.08 to $4.32, which is an increase of $3.24,
we set 0.09x = 3.24, which gives us x =36 dimes.
We subtract to find the 72 pennies.
Check: 36 x 10 + 72 = 360 + 72 = 432.