There is a total of 24 pupils. They donate a total of $230. If each boy donates $8 and each girl donates $10, how many girls and boys were there?

Let's denote the number of boys as $ b $ and the number of girls as $ g $.

We have two key pieces of information:

1. The total number of pupils is 24.
\[
b + g = 24
\]

2. The total amount of money donated is $230. Each boy donates $8, and each girl donates $10.
\[
8b + 10g = 230
\]

We now have a system of two equations:
\[
\begin{aligned}
1. & \ b + g = 24 \\
2. & \ 8b + 10g = 230
\end{aligned}
\]

### Step 1: Solve the first equation for $ b $:
\[
b = 24 - g
\]

### Step 2: Substitute $ b = 24 - g $ into the second equation:
\[
8(24 - g) + 10g = 230
\]

### Step 3: Distribute and simplify the equation:
\[
192 - 8g + 10g = 230
\]
\[
2g + 192 = 230
\]

### Step 4: Subtract 192 from both sides:
\[
2g = 38
\]

### Step 5: Divide by 2 to solve for $ g $:
\[
g = 19
\]

### Step 6: Substitute $ g = 19 $ back into the first equation to find $ b $:
\[
b + 19 = 24
\]
\[
b = 5
\]

So, there are 5 boys and 19 girls.

**Answer:** There are 5 boys and 19 girls.

Would you like further details or have any questions?

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Here are some related questions you might be interested in:

1. If the number of boys was doubled, how much would they donate in total?
2. What if each girl donated $12 instead of $10, keeping the number of pupils the same?
3. If there were 30 pupils instead of 24, how would that affect the donations?
4. How much more would the total donation be if each boy donated $10 instead of $8?
5. What would the total donation be if there were equal numbers of boys and girls?
6. If one more boy joined the group, how much would the total donation increase?
7. What percentage of the total donation was made by the girls?
8. How many pupils would be needed to donate $500 if each boy donates $8 and each girl donates $10?

**Tip:** When working with systems of equations, substituting one equation into another is a useful strategy to simplify and solve for the unknown variables.

Learn how to solve a problem involving donations by boys and girls where there are 5 boys and 19 girls in total. This problem requires understanding of systems of equations and is suitable for Grades 6-8 students.

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