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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:
 
x = 1 dime
y = 1 nickel
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 + y                = 148               [Eq. 1]
10x + 5y          = 1065             [Eq. 2]
 
Solving Eq. 1 for x gives:
 
x + y                = 148               [Eq. 1]
x                      = 148 – y         [Eq. 3]
 
Substituting Eq. 3 in Eq. 2 gives:
 
10x + 5y                      = 1065             [Eq. 2]
10(148 – y) + 5y          = 1065
1480 – 10y + 5y          = 1065
1480 – 5y                    = 1065
1480 – 1065                = 5y
415                              = 5y
415/5                           = y
83                                = y
 
Using Eq. 2 to solve for x:
 
10x + 5y          = 1065             [Eq. 2]
10x + 5(83)     = 1065
10x + 415        = 1065
10x                  = 1065 – 415
10x                  = 650
x                      = 650/10
x                      = 65
 
 
Therefore, there were 65 dimes and 83 nickels collected in the parking meter slot machine.
 
Check:
 
x + y                = 148               [Eq. 1]
[The total number of coins is 183]
 
65 + 83            = 148
148                  = 148
 
10x + 5y          = 1065             [Eq. 2]
[1065 cents means $10.65]
 
10(65) + 5(83) = 1065
1065                = 1656