A bank teller counted $100 and $50 bills. This totaled to 117 bills worth $9950. How many bills of each type did the teller have?

Question

*use linear equation in two variables

*please show solution

Answer 1

First, re-read the problem until you understand it and can put it into your own words.  How's this:  money in two denominations of bills; number of bills given; total value given.

 

Then, assign variables.  Let's assign mnemonic variables.  Let:

    H = number of $100 bills

    F = number of $50 bills

 

Note:  $100 * (the number of $100's) = the value of all the $100 bills; similarly with the $50's.

 

Translate:

   "totaled to 117 bills"     means             H + F = 117    (eq1)

   "worth $9950"       means     $100*H + $50*F = $9950      (eq2)

   "How many bills of each type did the teller have?"        means     report H and F

 

Now, the easy math (let's use the elimination method):

    100H  + 100F    =   11700              (100*eq1)

    100H  +  50F     =    9950               (eq2)

  ----------------------------------      (elimination; subtract equations)

                  50F    =     1750

                     F     =     35                 (eq3)

          H  +    F     =    117                (original eq1)

      -----------------------------       (elimination; subtract de3 from eq1)

          H               =     82

 

Checking (very important):

  Is  82 + 35 = 117   ?

          117 = 117   ? yes

  is  100*82 + 50*35 = 9950   ?

       8200 + 1750 = 9950   ?

             9950  = 9950   ? yes