Question

A parking meter contains nickels and quarters worth $7.70. There are 54 coins in all. Find how many of each there are.

Answer 1

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

$\frac{-0.24n}{-0.24} =\frac{-5.8}{-0.24}$

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.