He has 6 nickels and 9 dimes.
You can use the equations and suppose x = nickels and y = dimes:
x + y =15
0.05x + 0.1y = 1.20
You can check if it is correct by substituting x for 6 and y for 9 in both.
(6) + (9) = 15
6+ 9 = 15
15 = 15
0.05(6) + 0.1(9) = 1.20
0.3 + 0.9 = 1.20
1.20 = 1.20
Therefore, he has 6 nickels.
