Question
I’m hotel clerk counts his one dollar bills and $10 bills at the end of the day he finds that he has a total of 59 bills having a combined monetary value of $185 find the number of bills and each denomination that he has
Answers
You can either do this in one variable or 2.
If you do it in two variables you have two equations, that will need to be solved : )
Let x represent the one dollar bills and y the 10$ bills
x + y = 59 bills.
Now we have to deal with the value of the money for equation 2.
1x + 10y = 185
Now you have many ways to solve for x and y : )
If you do "substitution" you could re-arrange equation 1 to isolate x or y...
x = 59 - y
then sub that into your second equation and solve for y : )
Then once you have y sub it back into one of the original equations and solve for x.
If you do it in two variables you have two equations, that will need to be solved : )
Let x represent the one dollar bills and y the 10$ bills
x + y = 59 bills.
Now we have to deal with the value of the money for equation 2.
1x + 10y = 185
Now you have many ways to solve for x and y : )
If you do "substitution" you could re-arrange equation 1 to isolate x or y...
x = 59 - y
then sub that into your second equation and solve for y : )
Then once you have y sub it back into one of the original equations and solve for x.
He has X $1 bills.
Y $10 bills.
Eq1: x + y = 59.
Eq2: x + 10y = 185.
Multiply Eq1 by -1 and add Eq1 and Eq2:
-x - y = -59
x + 10y = 185
Sum: 9y = 126,
Y = 14.
In Eq1, replace y with 14 and solve for x.
Y $10 bills.
Eq1: x + y = 59.
Eq2: x + 10y = 185.
Multiply Eq1 by -1 and add Eq1 and Eq2:
-x - y = -59
x + 10y = 185
Sum: 9y = 126,
Y = 14.
In Eq1, replace y with 14 and solve for x.