Miguel has 52 coins in dimes and nickels totaling $4.50. how many of each coin does he have?

See what would happen if there was half and half (26 dimes and 26 nickels).

26 (.05) + 26 (.1) = 1.3+2.6=3.9

There needs to be more;

There needs to be 14 nickels and 38 dimes.

14 (.05) + 38 (.1) =.7+3.8=4.5