SOLUTION: Mark has 45 cents in dimes and nickels. He has 3 more nickels than dimes. How many of each type of coin does Mark have? Write a system of equations, then solve.

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: Mark has 45 cents in dimes and nickels. He has 3 more nickels than dimes. How many of each type of coin does Mark have? Write a system of equations, then solve.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 936304: Mark has 45 cents in dimes and nickels. He has 3 more nickels than dimes. How many of each type of coin does Mark have? Write a system of equations, then solve.
Found 2 solutions by AnlytcPhil, Alan3354:
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Mark has 45 cents in dimes and nickels. He has 3 more nickels than dimes. How many of each type of coin does Mark have? Write a system of equations, then solve. 
Let the number of nickels be x
Let the number of dimes be y 
 
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
NICKELS      x        $0.05    $0.05x 
DIMES        y        $0.10    $0.10y
-------------------------------------------
                         TOTAL $0.45

He has 3 more nickels than dimes.
  %28matrix%283%2C1%2CNumber%2Cof%2Cnickels%29%29%22%22=%22%22%28matrix%283%2C1%2CNumber%2Cof%2Cdimes%29%29%22%22%2B%22%223%29%29

        x = y + 3

That's the first equation.  To get the second equation:

  %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%284%2C1%2CTotal%2Cvalue%2Cof%2Ccoins%29%29

            x = y + 3
0.05x + 0.10y = 0.45  

Get rid of decimals by multiplying every term of 2nd 
equation by 100

              x = y + 3
       5x + 10y = 45

Substitute y + 3 for x in the second equation:

 5(y + 3) + 10y = 45
  5y + 15 + 10y = 45
       15y + 15 = 45
            15y = 30
              y = 2

Substitute 2 for y in  

              x = 2 + 3 
              x = 5

So he has 5 nickels and 2 dimes. 

Edwin

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Mark has 45 cents in dimes and nickels. He has 3 more nickels than dimes. How many of each type of coin does Mark have? Write a system of equations, then solve.
==========
Another method:
Put the "3 more nickels" to the side.
What's left is an equal # of Ns and Ds worth 30 cents.
Each pair is 15 cents.
30/15 = 2 pairs
--> 2 dimes and 5 nickels