SOLUTION: Mike gave his friend 53 coins that total $3.65. He gave him nickels and dimes. How many nickels and dimes there Mike give his friend?

Algebra ->  Systems-of-equations -> SOLUTION: Mike gave his friend 53 coins that total $3.65. He gave him nickels and dimes. How many nickels and dimes there Mike give his friend?      Log On


   

Question 961845: Mike gave his friend 53 coins that total $3.65. He gave him nickels and dimes. How many nickels and dimes there Mike give his friend?
Answer by AnlytcPhil(1810) About Me  (Show Source):
You can put this solution on YOUR website!

Let the number of nickels be x
Then the number of dimes, using
ONE PART = TOTAL MINUS OTHER PART,
is 53-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels      x         $0.05    $0.05x
dimes      53-x        $0.10    $0.10(53-x)
-------------------------------------------
TOTALS      53        -----     $3.65

 The equation comes from the column on the right

  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Cnickels%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cdimes%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29

 0.05x + 0.10(53-x) = 3.65

Get rid of decimals by multiplying every term by 100:

     5x + 10(53-x) = 365

    5x + 530 - 10x = 365

         -5x + 530 = 365

               -5x = -165

                 x = 33 = the number of nickels.

The number of dimes is 53-x or 53-33 or 20 dimes.

Checking:  33 nickels is $1.65 and 20 dimes is $2.00
            That's 53 coins.
            And indeed $1.65 + $2.00 = $3.65
Edwin