SOLUTION: A jar has quarter and nickels with 76 coins. Total value is 10.80. Find the amount quarter and nickels

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Question 1028601: A jar has quarter and nickels with 76 coins. Total value is 10.80. Find the amount quarter and nickels
Found 2 solutions by Edwin McCravy, fractalier:
Answer by Edwin McCravy(20081)   (Show Source): You can put this solution on YOUR website!

Let the number of quarters be x
Let the number of nickels be y

                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
quarters      x       $0.25      $0.25x
nickels       y       $0.05      $0.05y
-------------------------------------------
TOTALS       76       -----     $10.80

 The first equation comes from the second column.

  

                 x + y = 76

 The second equation comes from the last column.
  

         0.25x + 0.05y = 10.8

Get rid of decimals by multiplying every term by 100:

          25x + 5y = 1080

 So we have the system of equations:
       .

We solve by substitution.  Solve the first equation for y:

           x + y = 76
               y = 76 - x

Substitute (76 - x) for y in 25x + 5y = 1080

    25x + 5(76 - x) = 1080
     25x + 380 - 5x = 1080
          20x + 380 = 1080
                20x = 700
                  x = 35 = the number of quarters.

Substitute in y = 76 - x
              y = 76 - (35)
              y = 41 nickels.

Checking:  35 quarters is $8.75 and 41 nickels is $2.05
            That's 76 coins.
            And indeed $8.75 + $2.05 = $10.80
Edwin
Answer by fractalier(6550)   (Show Source): You can put this solution on YOUR website!
Call the number of quarters and nickels, q and n.
Then we write
q + n = 76 and the value equation is
25q + 5n = 1080 (we work in cents)
Now multiply the top one by five and subtract...we get
25q + 5n = 1080
-(5q + 5n = 380)
-----------------
20q = 700
q = 35 quarters which means there are
n = 41 nickels
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