SOLUTION: Mr. Taylor withdrew $220 from the bank. The bank teller gave Mr. Taylor 16 bills, which were all $10 bills and $20 bills. How many $10 bills and how many $20 bills did the bank tel

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Mr. Taylor withdrew $220 from the bank. The bank teller gave Mr. Taylor 16 bills, which were all $10 bills and $20 bills. How many $10 bills and how many $20 bills did the bank tel      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1006041: Mr. Taylor withdrew $220 from the bank. The bank teller gave Mr. Taylor 16 bills, which were all $10 bills and $20 bills. How many $10 bills and how many $20 bills did the bank teller give Mr. Taylor?
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of $10 bills be x
Let the number of $20 bills be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
bill        bills      bill      bills
-------------------------------------------
$10 bills     x        $10      $10x
$20 bills     y        $20      $20y
-------------------------------------------
TOTALS       16      -----      $220

 The first equation comes from the second column.

  %28matrix%283%2C1%2CNumber%2Cof%2C%2410+bills%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2C%2420+bills%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Cbills%29%29

                 x + y = 16

 The second equation comes from the last column.
  %28matrix%284%2C1%2CValue%2Cof%2CALL%2C%2410+bills%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2C%2420+bills%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Cbills%29%29


             10x + 20y = 220

 So we have the system of equations:
           system%28x+%2B+y+=+16%2C10x+%2B+20y+=+220%29.

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

                x + y = 16
                    y = 16 - x

Substitute (16 - x) for y in 10x + 20y = 220

     10x + 20(16 - x) = 220
      10x + 320 - 20x = 220
           -10x + 320 = 220
                -10x = -100
                   x = 10 = the number of $10 bills.

Substitute in y = 16 - x
              y = 16 - (10)
              y = 6 $20 bills.

Checking:  10 $10 bills is $100 and 6 $20 bills is $120
            That's 16 bills.
            And indeed $100 + $120 = $220
Edwin