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Let's solve the problem step by step.

### Problem:
A group of 3 adults and 10 children bought tickets to watch a dance performance. Each adult ticket costs $7 more than each child ticket. The group paid a total of $125. What was the cost of each child ticket?

### Solution:

Let's define:
- $ x $ = cost of each child ticket in dollars.
- $ x + 7 $ = cost of each adult ticket in dollars.

#### Step 1: Write the equation for the total cost
The total cost can be written as the sum of the cost for adult tickets and child tickets.

- Cost of adult tickets = $ 3 \times (x + 7) $
- Cost of child tickets = $ 10 \times x $

Given that the total cost is $125, we can write the equation:
\[
3(x + 7) + 10x = 125
\]

#### Step 2: Simplify the equation
Distribute and combine like terms:
\[
3x + 21 + 10x = 125
\]
\[
13x + 21 = 125
\]

#### Step 3: Solve for $ x $
Subtract 21 from both sides:
\[
13x = 104
\]
Divide both sides by 13:
\[
x = 8
\]

So, the cost of each child ticket is **$8**.

### Verification:
- Cost of each adult ticket = $ x + 7 = 8 + 7 = 15 $
- Total cost for adults = $ 3 \times 15 = 45 $
- Total cost for children = $ 10 \times 8 = 80 $
- Total cost = $ 45 + 80 = 125 $

This confirms that our solution is correct.

Would you like more details or have any questions? Here are some related questions:

1. How would the total cost change if there were 4 adults instead of 3?
2. What would be the total cost if the price of a child ticket increased by $2?
3. If the total cost was $150 instead of $125, how would that affect the price of the child ticket?
4. What if each adult ticket was $5 more than the child ticket instead of $7, how would you adjust the calculation?
5. How much would the total be if there were 5 adults and 12 children?

**Tip:** When dealing with word problems, clearly define your variables and set up an equation based on the relationships given in the problem.

A group of 3 adults and 10 children bought tickets to watch a dance performance. Each adult ticket costs $7 more than each child ticket. The group paid a total of $125. What was the cost of each child ticket?

Learn how to determine the cost of each child ticket when a group of 3 adults and 10 children bought tickets to a dance performance. The solution involves algebraic concepts such as linear equations. Suitable for students in Grades 6-8.

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