A problem I need help with.

Question

A motel clerk counts his 1$ and 10$ bills at the end of a day. He finds that he has a total of 59 bills having a combined monetary value of $167. Find the number of bills of each denomination that he has.

 

assign two variables, X and Y. Set up  a system of Equations and solve.

Answer 1

Hello Aidan,

 

Two ways to figure this one out:

 

1) Forget X and Y -- you only need one variable.

 

Let x = # of $1 bills.

 

Then 59-x = # of $10 bills, right? NO SECOND VARIABLE.

 

Go right to the solution in one equation:

 

$1*x + $10(59-x) = $167, or

 

9x = 590-167 = 423. (Notice how all the $ signs cancelled out...)

 

Thus x = 47.

 

You have $47 in singles, and $120 in tens.

 

2) Your "system of equations" will have

 

x + y = 59, and

x + 10y = 167.

 

You could use this system and  subtract the first equation from the second to get

 

9y = 108 and y = 12, thus x = 59-12 = 47.

 

Either way, the terrorists lose.

 

 

Eric Moline

McMinnville OR

Answer 2

x=# of $1 bills

y=# of $10 bills

x+y=59

1*x+10*y=167

x+10y=167

x+y=59

subtract the equations to eliminate the x variable

9y=108

y=108/9

y=12 $10 bills ($120)

59-12=47 $1 bills ($47)

$120+$47=$167