Question

Michael's bank contains only nickels, dimes, and quarters. There are 63 coins in all, valued at $5.50. The number of nickels is 5 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

Answer 1

n + d + q = 63
n = 3(d + q) - 5
substitute and you now have only 2 variables.

5n + 10d + 25q = 550
again sub in
n = 3(d + q) - 5
and you have another equation in 2 variables only

solve those 2 equations in 2 unknowns.

Answer 2

N+D+Q=63
N+5=3(D+Q) or N-3D-3Q=-5
5N+10D+25Q=550

Solve it as you wish, I would use augmented matrix https://www.emathhelp.net/calculators/algebra-2/system-of-linear-equations-calculator/?s=N%2BD%2BQ%3D63%2C+N-3D-3Q%3D-5%2C+5N%2B10D%2B25Q%3D550&method=j&steps=on
N+D+Q=63, N-3D-3Q=-5, 5N+10D+25Q=550