SOLUTION: Mackenzie has 19 coins in her pocket. They are all either dimes or quarters, totaling $3.40. How many coins are quarters? Solve the word problem by creating a system of equat

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: Mackenzie has 19 coins in her pocket. They are all either dimes or quarters, totaling $3.40. How many coins are quarters? Solve the word problem by creating a system of equat      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 924248: Mackenzie has 19 coins in her pocket. They are all either dimes or quarters, totaling $3.40.
How many coins are quarters?
Solve the word problem by creating a system of equations. Use substitution to find the solution.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Mackenzie has 19 coins in her pocket. They are all either dimes or quarters, totaling $3.40.
Let the number of dimes be D
Let the number of dimes be Q   
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
DIMES        D        $0.10    $0.10D 
QUARTERS     Q        $0.25    $0.25Q
-------------------------------------------
TOTALS      19        -----    $3.40

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

%28matrix%283%2C1%2CNumber%2Cof%2Cdimes%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2Cquarters%29%29 %22%22=%22%22 %28matrix%283%2C1%2CNumber%2Cof%2Ccoins%29%29


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

system%28D%2BQ=19%2C%0D%0A%0D%0A0.10D+%2B+0.25Q+=+3.40%29

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

    10D + 25Q = 340

system%28D%2BQ=19%2C%0D%0A%0D%0A10D+%2B+25Q+=+340%29

Solve the first for D

D+Q=19
  D=19-Q

Substitute in

     10D + 25Q = 340
10(19-Q) + 25Q = 340
 190-10Q + 25Q = 340
       190+15Q = 340
           15Q = 150 
             Q = 10 quarters

             D = 19-Q = 19-10 = 9 dimes

Edwin