Define X as the number of dimes that John used. Just a reminder, dimes are 10 cents coins. The number of quarters that he used is (55−X). We can write the following equation: 10X+25(55−X)=1000. Notice that 1000 is the money he spent in cents. Therefore −15X=−375,X=25. The number of dimes is 25 and the number of quarters is 55−25=30. The difference between the amounts is 5 coins.