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.
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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.
