Give me every step to solve the following question:
A purse contains 18 coins, which includes $5 coins and $10 coins only. If the total value of the coins is $110,find the total number of $10 coins in the purse. Let X be the amount of $10 coins in the purse.

To solve the problem, we will set up and solve an equation using the information given.

### Problem Statement Recap:
- You have 18 coins in total, consisting of $5 coins and $10 coins.
- The total value of the coins is $110.
- Let $ X $ be the number of $10 coins.

### Steps to Solve:

1. **Define the Variables**:
   - Let $ X $ be the number of $10 coins.
   - Therefore, the number of $5 coins will be $ 18 - X $, because the total number of coins is 18.

2. **Write the Equation for the Total Value**:
   - The value contributed by the $10 coins is $ 10 \times X $.
   - The value contributed by the $5 coins is $ 5 \times (18 - X) $.

   The total value of all the coins is given as $110. Thus, the equation is:
   \[
   10X + 5(18 - X) = 110
   \]

3. **Expand and Simplify the Equation**:
   Distribute the 5 in the equation:
   \[
   10X + 90 - 5X = 110
   \]

4. **Combine Like Terms**:
   Combine the terms involving $ X $ on the left side:
   \[
   5X + 90 = 110
   \]

5. **Isolate $ X $**:
   Subtract 90 from both sides of the equation to isolate the term involving $ X $:
   \[
   5X = 20
   \]

6. **Solve for $ X $**:
   Divide both sides of the equation by 5:
   \[
   X = 4
   \]

### Conclusion:
The total number of $10 coins in the purse is $ \boxed{4} $.

### Verification:
- If there are 4 $10 coins, the total value from them is $ 4 \times 10 = 40 $ dollars.
- The remaining 14 coins must be $5 coins, giving a total value of $ 14 \times 5 = 70 $ dollars.
- The total value is $ 40 + 70 = 110 $ dollars, which matches the given total value.

Would you like to explore more details or have any questions about this problem?

Here are five additional questions related to this problem:
1. What if the total number of coins was different, say 20 coins, but the total value remained $110?
2. How would the solution change if the purse contained $1 coins instead of $5 coins?
3. If the number of $5 coins is tripled, what would be the new total value of all the coins?
4. How can you represent the problem using a system of equations instead of just one equation?
5. What is the value of the $10 coins if there were 5 instead of 4?

**Tip:** When solving word problems, clearly define your variables and ensure that each term in your equation accurately reflects the problem's conditions.

Learn how to solve the problem of determining the number of $10 coins in a purse containing $5 and $10 coins. Follow a detailed step-by-step solution including defining variables, setting up equations, and solving for the number of $10 coins. Suitable for students in Grades 7-9.

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