at the movie theater, child admission is $5.30 and adult admission is $8.60. On tuesday 152 tickets were sold for a total sales of $1030.00. how many child tickets were sold that day

Let $ x $ be the number of child tickets sold and $ y $ be the number of adult tickets sold.

We are given the following information:

1. The total number of tickets sold is 152:
   \[
   x + y = 152
   \]
2. The total sales amount to $1030.00, with child tickets priced at $5.30 and adult tickets priced at $8.60:
   \[
   5.30x + 8.60y = 1030
   \]

Now, we have a system of two equations:
\[
x + y = 152
\]
\[
5.30x + 8.60y = 1030
\]

We can solve this system using substitution or elimination. First, let's solve the first equation for $ y $:
\[
y = 152 - x
\]

Substitute this into the second equation:
\[
5.30x + 8.60(152 - x) = 1030
\]

Now simplify and solve for $ x $:
\[
5.30x + 8.60 \times 152 - 8.60x = 1030
\]
\[
5.30x + 1307.2 - 8.60x = 1030
\]
\[
-3.30x + 1307.2 = 1030
\]
\[
-3.30x = 1030 - 1307.2
\]
\[
-3.30x = -277.2
\]
\[
x = \frac{-277.2}{-3.30}
\]
\[
x = 84
\]

Thus, 84 child tickets were sold.

Would you like further details or explanations? Here are five related questions to deepen your understanding:

1. How many adult tickets were sold on that day?
2. Can this problem be solved using matrices?
3. What if the prices of child and adult tickets were switched?
4. How would the system change if there were more types of tickets?
5. How could you solve this graphically?

**Tip**: Solving systems of equations can be simplified by substitution or elimination methods—whichever seems easier for the given problem!

At the movie theater, child admission is $5.30 and adult admission is $8.60. On Tuesday, 152 tickets were sold for a total sales of $1030.00. How many child tickets were sold that day?

Learn how to solve a system of linear equations to determine how many child and adult tickets were sold at a movie theater. The problem involves algebraic concepts, such as substitution and elimination, and applies real-world prices for child and adult admissions. Suitable for students in Grades 8-10.

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