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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.

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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

[tex]x + 10 (53 - x) = 182[/tex]

[tex]x + 530 - 10x = 182[/tex]

[tex] -9x + 530 = 182[/tex] (subtract 530 on both sides)

-9x= -348

[tex]x=\frac{116}{3}[/tex]

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

We know y = 53 - x

[tex]y = 53 - \frac{116}{3} = \frac{43}{3}[/tex]



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