A school put on a music program.  Adult tickets were sold for $5.50 each, and child tickets were sold for $3.00 each.  The school collected $1,531.00 from ticket sales.  If a total of 347 tickets were sold, how many were adult tickets and how many were child tickets?

Let's define variables for the number of adult tickets and child tickets sold.

- Let $ a $ be the number of adult tickets sold.
- Let $ c $ be the number of child tickets sold.

We know the following two things:

1. The total number of tickets sold was 347. So,
   \[
   a + c = 347
   \]
2. The total money collected was $1,531. Since adult tickets were sold for $5.50 each and child tickets for $3.00 each, the total revenue equation is:
   \[
   5.50a + 3.00c = 1531
   \]

Now we have a system of two equations:
\[
1. a + c = 347
\]
\[
2. 5.50a + 3.00c = 1531
\]

### Solving the system of equations:
We can solve this system using substitution or elimination. Let's use substitution.

From equation 1:
\[
a = 347 - c
\]

Substitute $ a = 347 - c $ into equation 2:
\[
5.50(347 - c) + 3.00c = 1531
\]
Now, solve for $ c $:
\[
5.50 \times 347 - 5.50c + 3.00c = 1531
\]
\[
1908.50 - 5.50c + 3.00c = 1531
\]
\[
1908.50 - 2.50c = 1531
\]
\[
-2.50c = 1531 - 1908.50
\]
\[
-2.50c = -377.50
\]
\[
c = \frac{-377.50}{-2.50} = 151
\]

So, $ c = 151 $ child tickets were sold.

Now, substitute $ c = 151 $ back into equation 1:
\[
a + 151 = 347
\]
\[
a = 347 - 151 = 196
\]

Thus, $ a = 196 $ adult tickets were sold.

### Conclusion:
- 196 adult tickets were sold.
- 151 child tickets were sold.

Would you like further details or have any questions? Here are 5 related questions for practice:

1. If the child ticket price was increased to $4.00, how much money would be collected from 151 child tickets?
2. How much money would be collected if only adult tickets were sold for a similar event?
3. If the total number of tickets sold was reduced to 300, how would that affect the number of adult and child tickets?
4. How would the solution change if the total revenue was increased to $2,000?
5. How many more child tickets would need to be sold to match the revenue of 200 adult tickets?

**Tip:** When solving systems of equations, substitution works best when one equation is easily solved for a single variable.

A school put on a music program. Adult tickets were sold for $5.50 each, and child tickets were sold for $3.00 each. The school collected $1,531.00 from ticket sales. If a total of 347 tickets were sold, how many were adult tickets and how many were child tickets?

Learn how to solve a system of equations based on ticket sales for a school music program. Adult tickets were sold for $5.50, and child tickets for $3.00. With 347 total tickets sold and $1,531 collected, find out how many adult and child tickets were sold. Suitable for Grades 8-10.

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