Question

A motel clerk counts his​ $1 and​ $10 bills at the end of the day. He finds that he has a total of 53 bills having a combined monetary value of ​$ 182. Find the number of bills of each denomination that he has.

The clerk has___ ones and ___ Tens.

Answer 1

A motel clerk counts his​ $1 and​ $10 bills at the end of the day. He finds that he has a total of 53 bills having a combined monetary value of ​$ 182.

let x be the number of $1 bills

y be the number of $10 bills

There are total of 53 bills so the equation becomes

x+y=53 ---> first equation

Bills having a combined monetary value of ​$ 182

x + 10 y = 182 ----> second equation

Now we solve for x and y

x+y=53

y = 53 - x

Now plug in 53 - x in second equation

`x + 10 (53 - x) = 182`

`x + 530 - 10x = 182`

`-9x + 530 = 182` (subtract 530 on both sides)

-9x= -348

`x=(116)/(3)`

Recheck the numbers given in the question. because we got answer in fraction form.

We know y = 53 - x

`y = 53 - (116)/(3) = (43)/(3)`