SOLUTION: Kevin and Randy Muise have a jar containing 79 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $10.35. How many of each type of coins

Question 924214: Kevin and Randy Muise have a jar containing 79 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $10.35. How many of each type of coins do they have?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
Kevin and Randy Muise have a jar containing 79 coins, all of which are either
quarters or nickels. The total value of the coins in the jar is $10.35. How many
of each type of coins do they have?

Let the number of nuckels be N
Let the number of dimes be Q   
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
NICKELS      N        $0.05    $0.05N 
QUARTERS     Q        $0.25    $0.25Q
-------------------------------------------
TOTALS      79        -----    $10.35

 The equations comes from the "Number of coins" column 
and the "Value of ALL coins" column:

  






Get rid of decimals in the second by multiplying 
every term by 100

      5N + 25Q = 1035



Solve the first for N

N+Q=79
  N=79-Q

Substitute in

       5N + 25Q = 1035
  5(79-N) + 25Q = 1035
   395-5Q + 25Q = 1035
        395+20Q = 1035
            20Q =  640 
              Q =   32 quarters

              N = 79-Q = 79-32 = 47 nickels

Edwin

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