Question

I only need the equations, I can solve it.

Answer 1

You have a pile of 22 coins that includes nickels and dimes
Let n= nickels and d= dimes
total coins= nickels and dimes
n+d=22
The total value of the coins is $1.20
d=1.20-n
You would solve by system of equations.
n+d=22
d=1.20-n
I suggest using process of substitution

Answer 2

How can you solve it if you don't know the equations?  :P  Just kidding...

n+d=22, so we can say that d=22-n

5n+10d=120, and using d found above in this equation gives you:

5n+10(22-n)=120

5n+220-10n=120

-5n=-100

n=20, and since  d=22-n, d=2

So there are two dimes and twenty nickels...

check...

20(5)+2(10)=100+20=120 cents which is $1.20

n+d=22, 20+2=22, 22=22