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

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) (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:

  






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

    10D + 25Q = 340



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

RELATED QUESTIONS
john has 40 coins in his pocket. they are all dimes and quarters totaling $5.50. how many (answered by bogatto)

John has a total of 13 coins in his pocket. Of the 13 coins, they are all either quarters (answered by stanbon)

john has a total of 13 coins in his pocket. of the 13 coins they are all either quarters... (answered by Edwin McCravy)

John has a total of 13 coins in his pocket. Of the 13 coins, they are all either quarters (answered by solver91311)

mandy has 15 coins in her pocket that are either dimes or quarters. the value of her... (answered by Alan3354)

Cookie has 97 coins in her collection � all either nickels, dimes or quarters. If 77 of... (answered by Edwin McCravy)

john has a total of 13 coins in his pocket. of the 13 coins, they are all eithern... (answered by scott8148)

adam has quarters and dimes in his pocket. there are 28 coins in all, and they are worth... (answered by richwmiller)

Darrel has dimes and quarters in his pocket. He has 28 coins in all, and they are worth... (answered by ikleyn)