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Let's assume there is n number of nickels coin and q number of quaters coin.
Given that there are 54 coins in total. So, sum of n and q must be equal to 54.
So, n + q =54.
Hence, q = 54 - n ...(1)
Now 1 nickel is worth of $0.01 nickel. So, n nickel will woth of 0.01n.
Similarly q quarters will worth of 0.25q.
Given that a parking meter contains nickels and quarters worth $7.70. So, sum of 0.01n and 0.25q will be equal to 7.70. Therefore,
0.01n + 0.25q = 7.70
From equation (1) we can plug in q=54-n in the above equation. So,
0.01n + 0.25 (54-n) = 7.70
0.01n + 13.5 -0.25n = 7.70
-0.24n + 13.5 = 7.70
-0.24n = 7.70 - 13.5
-0.24n = -5.8
So, n= 24.167
Hence, n= 24 ( rounded to nearest integer).
Next step is to plug in n=24 in equation (1). So,
q = 54 - 24 = 30.
Hence, there will be 24 nickel and 30 quarter.