A motel clerk counts his $1 and $10 bills at the end of a day. He finds that he has atotal of 56 bills having acombined monetary value of $191. Find the number of bills of each denomination that he has
number of 10's ---- x
number of 1's ------56-x
10x + 1(56-x) = 191
9x = 135
x = 15
he has 15 tens and 41 ones
check:
15(10) + 41 = 191
To solve this problem, we can use a system of linear equations. Let's assign variables to represent the number of $1 bills and $10 bills:
Let's assume the number of $1 bills is x.
Let's assume the number of $10 bills is y.
We have two conditions to consider:
1. The total number of bills is 56: x + y = 56. (Equation 1)
2. The combined monetary value is $191: 1x + 10y = 191. (Equation 2)
We now have a system of two equations with two variables. We can solve this system to find the values of x and y.
From Equation 1, we can rearrange it to solve for x:
x = 56 - y.
Substituting the value of x into Equation 2, we get:
1(56 - y) + 10y = 191.
56 - y + 10y = 191.
56 + 9y = 191.
9y = 191 - 56.
9y = 135.
y = 135/9.
y = 15.
Now we can determine the value of x using either Equation 1 or Equation 2:
x = 56 - y.
x = 56 - 15.
x = 41.
Therefore, the motel clerk has 41 one-dollar bills and 15 ten-dollar bills.
Let's assume the number of $1 bills is x, and the number of $10 bills is y.
According to the information given, we have two equations to solve:
1. x + y = 56 (Eq.1) - Since the total number of bills is 56.
2. 1x + 10y = 191 (Eq.2) - Since the total monetary value of the bills is $191.
To solve the equations, we can use substitution or elimination method. Let's use the substitution method:
From Eq.1, x = 56 - y
Substituting this value of x in Eq.2:
1(56 - y) + 10y = 191
56 - y + 10y = 191
9y = 191 - 56
9y = 135
y = 135 / 9
y = 15
Now, substituting the value of y in Eq.1:
x + 15 = 56
x = 56 - 15
x = 41
Therefore, the motel clerk has 41 $1 bills and 15 $10 bills.