SOLUTION: you have $13.80 in quarters and dimes. if you have 84 coins, how many are dimes?

Question 1010672: you have $13.80 in quarters and dimes. if you have 84 coins, how many are dimes?

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

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


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
quarters     x        $0.25     $0.25x
dimes        y        $0.10     $0.10y
-------------------------------------------
TOTALS      84       -----      $13.80

 The first equation comes from the second column.

  

                 x + y = 84

 The second equation comes from the last column.
  

           0.25x + 0.10y = 13.80

Get rid of decimals by multiplying every term by 100:

               25x + 10y = 1380

 So we have the system of equations:
           .

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

           x + y = 84
               y = 84 - x

Substitute (84 - x) for y in 25x + 10y = 1380

   25x + 10(84 - x) = 1380
    25x + 840 - 10x = 1380
          15x + 840 = 1380
                15x = 540
                  x = 36 = the number of quarters.

Substitute in y = 84 - x
              y = 84 - (36
              y = 48 dimes.

Checking:  36 quarters is $9.00 and 48 dimes is $4.80
            That's 84 coins.
            And indeed $9.00 + $4.80 = $13.80
Edwin

RELATED QUESTIONS
How many dimes & quarters are in $19.75 if you have 100... (answered by josmiceli)

you have a piggy bank containing a total of 84 coins in dimes and quarters. If the piggy... (answered by XilliX)

You have 12 coins in quarters and dimes. If your coins total $1.95, how many of each do... (answered by Alan3354)

You have 13 coins worth $2.20. All your coins are dimes or quarters. How many of each do (answered by jorel1380)

You have $15.25 in quarters and dimes. You have 103 coins total. How many quarters do you (answered by mbogner)

if one has $11.00 in quarters and dimes with total of 80 coins, how many dimes does... (answered by checkley71)

You have 24 coins (either dimes or quarters only) in your pockets that are worth 4.50... (answered by erica65404)

You have 15 coins in your pocket. The coins are either quarters or dimes.You have a total (answered by ichigo449,richwmiller)

You have 15 coins in your pocket all quarters and dimes. They total up to $3.15. How many (answered by solver91311)