A cashier has a total of 121 bills, made up of fives and tens. The total value of the money is $935. How many ten-dollar bills does the cashier have?

Let the number of five-dollar bills be $ x $ and the number of ten-dollar bills be $ y $.

We are given two pieces of information:

1. The total number of bills is 121:
   \[
   x + y = 121
   \]

2. The total value of the money is $935:
   \[
   5x + 10y = 935
   \]

We can solve this system of equations to find $ y $.

### Step 1: Solve the first equation for $ x $
From $ x + y = 121 $, we can express $ x $ as:
\[
x = 121 - y
\]

### Step 2: Substitute $ x = 121 - y $ into the second equation
Substitute $ x = 121 - y $ into the equation $ 5x + 10y = 935 $:
\[
5(121 - y) + 10y = 935
\]

### Step 3: Simplify and solve for $ y $
Distribute the 5:
\[
5 \times 121 - 5y + 10y = 935
\]
\[
605 - 5y + 10y = 935
\]
Combine like terms:
\[
605 + 5y = 935
\]
Subtract 605 from both sides:
\[
5y = 330
\]
Divide by 5:
\[
y = 66
\]

Thus, the cashier has 66 ten-dollar bills.

### Conclusion
The cashier has **66 ten-dollar bills**.

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. How many five-dollar bills does the cashier have?
2. If the cashier had 150 bills, how would that affect the solution?
3. What if the total value of the money was $960 instead of $935?
4. If the cashier had 60 ten-dollar bills, how many five-dollar bills would they have?
5. How can you check if your solution to a system of equations is correct?

**Tip:** Always double-check your work by substituting your answers back into the original equations to verify that they satisfy both conditions.

Learn how to solve a system of linear equations to determine the number of ten-dollar bills a cashier has, given a total of 121 bills worth $935. This problem demonstrates key algebraic concepts, including substitution and solving systems of equations. Suitable for students in Grades 8-10.

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