SOLUTION: Angel was counting the coins in his bank. He found that he had 70 coins, which totaled $13.30. If he only had quarters and dimes, how many of each coin did he have? !

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Angel was counting the coins in his bank. He found that he had 70 coins, which totaled $13.30. If he only had quarters and dimes, how many of each coin did he have? !      Log On


   

Question 1024814: Angel was counting the coins in his bank. He found that he had 70 coins, which totaled $13.30. If he only had quarters and dimes, how many of each coin did he have?
!
Found 2 solutions by Edwin McCravy, Cromlix:
Answer by Edwin McCravy(20060) About Me  (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      70      -----      $13.30

 The first equation comes from the second column.

  %28matrix%283%2C1%2CNumber%2Cof%2Cquarters%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2Cdimes%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Ccoins%29%29

                     x + y = 70

 The second equation comes from the last column.
  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Cquarters%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

             0.25x + 0.10y = 13.30

Get rid of decimals by multiplying every term by 100:

                 25x + 10y = 1330

 So we have the system of equations:
           system%28x+%2B+y+=+70%2C25x+%2B+10y+=+1330%29.

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

                     x + y = 70
                         y = 70 - x

Substitute (70 - x) for y in 25x + 10y = 1330

          25x + 10(70 - x) = 1330
           25x + 700 - 10x = 1330
                 15x + 700 = 1330
                       15x = 630
                         x = 42 = the number of quarters.

Substitute in y = 70 - x
              y = 70 - (42)
              y = 28 dimes.


Checking:  42 quarters is $10.50 and 28 dimes is $2.80
            That's 70 coins.
            And indeed $10.50 + $2.80 = $13.30
Edwin

Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
Make dimes = x
quarters = y
x + y = 70......(1)
10x + 25y = 1330.....(2)Multiply Eq(1) by 25
25x + 25y = 1750....(1)
10x + 25y = 1330.....(2)
Subtract Eq(2) from Eq(1)
15x = 420
x = 420/15
x = 28
Substitute x = 28 into Eq(1)
x + y = 70
28 + y = 70
y = 70 - 28
y = 42
angel had 28 dimes and 42 quarters.
Hope this helps :-)