Shehkar pulls 31 coins out of his pocket. each coin is either a dime or a quarter. if he has a total of 5.95, how many dimes does he have?

1 Answer
Jul 20, 2018

Answer:

19 quarters, 12 dimes.

Explanation:

Let #d# be the number of dimes and #q# be the number of quarters.

We can set up a simple pair of equations from the question. We know that the total number of coins is 31, hence
#d + q = 31 or d = 31-q #

We also know how much they cost, so
#10d + 25q = 595 #

We can plug the first equation into the second, replacing d with the formula we got:
#10(31-q) + 25q = 595 #
#310 - 10q + 25q = 595 #
#15q = 285 implies q = 19 #

Since there are 19 quarters, there must be #31-19 = 12# dimes.

We can check this:

19 quarters add up to $4.75. 12 dimes add up to $1.20. Put em together and you get $5.95.