SOLUTION: motel clerk counts his $1 and $10 bills at the end of the day. He finds that he has a totalof 60 bills having a combined monetary value of $143. find the number of bills of each'

Algebra ->  Equations -> SOLUTION: motel clerk counts his $1 and $10 bills at the end of the day. He finds that he has a totalof 60 bills having a combined monetary value of $143. find the number of bills of each'      Log On


   

Question 1015519: motel clerk counts his $1 and $10 bills at the end of the day. He finds that he has a totalof 60 bills having a combined monetary value of $143. find the number of bills of each'
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of Ones be x
Let the number of Tens be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        bills      bill      bills
-------------------------------------------
Ones         x          $1     $1x
Tens         y         $10     $10y
-------------------------------------------
TOTALS       60      -----     $143

 The first equation comes from the second column.

  %28matrix%283%2C1%2CNumber%2Cof%2COnes%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2CTens%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Cbills%29%29
                 x + y = 60

 The second equation comes from the last column.
  %28matrix%284%2C1%2CValue%2Cof%2CALL%2COnes%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2CTens%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Cbills%29%29

           1.00x + 10.00y = 1430

                  x + 10y = 143

 So we have the system of equations:
           system%28x+%2B+y+=+60%2Cx+%2B+10y+=+143%29.

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

           x + y = 60
               y = 60 - x

Substitute (60 - x) for y in 1x + 10y = 143

    1x + 10(60 - x) = 143
     1x + 600 - 10x = 143
          -9x + 600 = 143
                -9x = -457
                  x = 50 7/9 = the number of Ones.

So you must have a fraction of a bill.  That's not possible.

No solution.  Did you type a number wrong?  I'll go ahead
and finish the problem as you have stated it. 
 
Substitute in y = 60 - x
              y = 60 - (50 7/9)
              y = 9 2/9 Tens.

Checking:  50 7/9 Ones is $50.77 7/9 and 9 2/9 Tens is $92.22 2/9
            That's 60 coins.
            And indeed $50.77 7/9 + $92.22 2/9 = $1430

So the algebra is correct.  Trouble is you can't tear a bill in
parts and the parts equal to that fraction of the bill's worth.

So, just maybe you copied the problem wrong, don't you think?

Edwin