Casey has $21.40 in dimes and quarters. she has a total of 100 coins. how much of each coin does casey have?

If they were all dimes, Casey would have $10.00. Casey has $11.40 more than that. Each quarter coin (that replaces a dime) adds $0.15 to the total, so there must be ...

... $11.40/$0.15 = 76

quarters.

Then the number of dimes is 100 -76 = 24.

Solution using equation

If you want an equation, let the variable represent the number of higher-value coin: quarters. Then the total value is ...

... (100 -q)×0.10 + q×0.25 = 21.40

... 10.00 +0.15q = 21.40

... q = (21.40 -10.00)/0.15 = 76 . . . . . . you should be able to see the similarity to the verbal description above.