Michael's Bank Contains Only Nickels, Dimes, and Quarters $\$$ 420 the Number of Nickels Is 10 Short of Being

Multiple Choice

Michael's bank contains only nickels, dimes, and quarters. There are 46 coins in all, valued at $\$$ 4.20. The number of nickels is 10 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

A) 8 dimes
B) 11 dimes
C) 6 dimes
D) 32 dimes