# A parking meter slot receives dimes and nickels

A parking meter slot receives dimes and nickels. When the meter box was emptied there were 148 coins and a total of $ 10.65. How many dimes and how many nickels were there?

**Solution:**

Based on the details given in the problem, we can have this representation:

**= 1 dime**

*x***= 1 nickel**

*y*1 dime = 10 cents = 10/100 dollar = 0.1 dollar

1 nickel = 5 cents = 5/100 dollar = 0.05 dollar

10.65 dollars = 10.65(100) = 1065 cents

With the given data, we can derive the following equations:

**+**

*x***= 148 [Eq. 1]**

*y*10

**+ 5***x***= 1065 [Eq. 2]***y*Solving Eq. 1 for

**gives:***x***+**

*x***= 148 [Eq. 1]**

*y***= 148 – y [Eq. 3]**

*x*Substituting Eq. 3 in Eq. 2 gives:

10

**+ 5***x***= 1065 [Eq. 2]***y*10(148 – y) + 5

**= 1065***y*1480 – 10y + 5y = 1065

1480 – 5y = 1065

1480 – 1065 = 5y

415 = 5y

415/5 = y

83 = y

Using Eq. 2 to solve for x:

10

**+ 5***x***= 1065 [Eq. 2]***y*10

**+ 5(83) = 1065***x*10

**+ 415 = 1065***x*10

**= 1065 – 415***x*10

**= 650***x***= 650/10**

*x***= 65**

*x*Therefore, there were 65 dimes and 83 nickels collected in the parking meter slot machine.

**Check:**

**+**

*x***= 148 [Eq. 1]**

*y*[

*The total number of coins is 183*]**+**

*65***= 148**

*83*148 = 148

10

**+ 5***x***= 1065 [Eq. 2]***y*[

*1065 cents means $10.65*]10

**+ 5***(65)***= 1065***(83)*1065 = 1656