1170.21 – Money Bag

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 by 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 xx dimes, the amount goes up by 0.09x0.09x.

So to increase the amount of money from $1.08 to $4.32, which is an increase of $3.24, we set 0.09x=3.240.09x = 3.24, which gives us x=36x = 36 dimes.

We subtract to find the 72 pennies.

Check: 36×10+72=360+72=43236 \times 10 + 72 = 360 + 72 = 432.