John cashed a check for $630. The teller gave him three 50-dollar bills, eighteen 20-dollar bills, and t 10-dollar bills. Determine the value of t. 

Let's solve this problem by setting up an equation to represent the total amount of money John received in different denominations:

1. **Amount from 50-dollar bills**: John received three 50-dollar bills, so:
   \[
   3 \times 50 = 150 \text{ dollars}
   \]

2. **Amount from 20-dollar bills**: John received eighteen 20-dollar bills, so:
   \[
   18 \times 20 = 360 \text{ dollars}
   \]

3. **Amount from 10-dollar bills**: Let $ t $ be the number of 10-dollar bills. Therefore, the total amount from the 10-dollar bills is:
   \[
   10 \times t
   \]

4. **Total amount**: The total cash John received is $630, so we set up the following equation:
   \[
   150 + 360 + 10t = 630
   \]

5. **Solve for $ t $**:
   \[
   510 + 10t = 630
   \]
   \[
   10t = 630 - 510
   \]
   \[
   10t = 120
   \]
   \[
   t = \frac{120}{10} = 12
   \]

So, the value of $ t $ is $ 12 $. John received **twelve 10-dollar bills**.

Would you like more details on any step?

Here are 5 related questions:
1. What if John received four 50-dollar bills instead of three?
2. How would the solution change if he cashed a check for $700 with the same denominations?
3. What if he received an additional denomination, such as 5-dollar bills?
4. Can we solve for $ t $ if the total amount is unknown?
5. How can we verify the total amount from the solution?

**Tip:** When solving for variables in word problems, translating denominations into equations helps simplify the setup.

John cashed a check for $630. The teller gave him three 50-dollar bills, eighteen 20-dollar bills, and t 10-dollar bills. Determine the value of t.

Solve how many 10-dollar bills John received when he cashed a check for $630, given the amounts in 50-dollar and 20-dollar bills. This problem demonstrates algebraic concepts suitable for middle school students, involving basic linear equations.

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