n = the number of nickels
p = the number of pennies
Total number of coins she has = 22.
n + p = 22
First equation
Each penny is one cent and a nickel is worth 5 cents
And the total is $0.54
Second equation. 0.05n + 0.01p = 0.54
n + p = 22
0.05n + 0.01p = 0.54
Multiply the top equation by -0.05 which gives us
-0.05n - 0.05p = -1.1
0.05n + 0.01p = 0.54
The n terms cancel out which leaves the p value
-0.04p = -0.56
Divide by the -0.04p and you get p=14
Substitute the value of p back into the top equation.
Which is n + 14 = 22
Subtract 14 and you get n = 8
Ari has 8 nickels and 14 pennies