Jack has twelve coins in his pocket made up of dimes and quarters. he has a total value of $1.95. how many of each are there

Since $1.95 ends in a five, and the only way to get that is with an odd number of quarters (dimes are always .10, and even numbers of quarters also end in zero(.50)), we know we are looking at an odd number of quarters.  Then we can use the guess and test method to quickly find our answer.

5 quarters = $1.25
7 dimes = $0.70

Total: 12 coins = $1.95