12 girls and a certain number of boys collected an average of 25 stickers. The girls collected an average of 20 stickers. Each boy collected an average of 7 more stickers than each girl. How many children were there altogether?

We are given the following information:

- There are 12 girls.
- The girls collected an average of 20 stickers each.
- The boys collected an average of 7 more stickers than the girls, meaning each boy collected an average of \(20 + 7 = 27\) stickers.
- The total average number of stickers collected by all the children is 25.

Let the number of boys be denoted by \( b \).

### Step 1: Total stickers collected by girls
The total number of stickers collected by the 12 girls is:
\[
\text{Total stickers by girls} = 12 \times 20 = 240 \, \text{stickers}.
\]

### Step 2: Total stickers collected by boys
The total number of stickers collected by the \( b \) boys is:
\[
\text{Total stickers by boys} = b \times 27.
\]

### Step 3: Total number of children
The total number of children is:
\[
\text{Total children} = 12 + b.
\]

### Step 4: Set up an equation for the average stickers collected
The average number of stickers collected by all children is 25. Therefore, the total stickers collected by both girls and boys, divided by the total number of children, should be 25:
\[
\frac{240 + 27b}{12 + b} = 25.
\]

### Step 5: Solve the equation
Now, let's solve this equation step by step:
\[
240 + 27b = 25(12 + b),
\]
\[
240 + 27b = 300 + 25b,
\]
\[
27b - 25b = 300 - 240,
\]
\[
2b = 60,
\]
\[
b = 30.
\]

### Step 6: Total number of children
The total number of children is:
\[
12 + 30 = 42.
\]

Thus, there are **42 children** altogether.

Do you need further details on any part of the explanation? Here are five related questions to explore:

1. How would the total number of children change if each boy collected 5 more stickers than each girl instead of 7?
2. What would happen to the total number of stickers if there were 5 fewer boys?
3. If the average sticker count for the boys was raised to 30, how would that affect the total number of children?
4. What if the girls collected an average of 25 stickers each? How would that change the equation?
5. How can we verify that the total number of stickers collected matches the given average?

**Tip**: When solving problems involving averages, setting up the equation with the total sum is crucial for simplifying the problem.

Explore how to solve a problem involving averages where 12 girls and a certain number of boys collect stickers. This problem utilizes algebraic equations to determine the total number of children, focusing on averages and differences between groups. Suitable for students in Grades 6-8.

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