A movie theater charges $5 admission for an adult and $3 for a child. If 700 tickets were

sold and the total revenue received was $2900, how many tickets of each type were sold?

To solve this problem, we need to set up a system of equations based on the given information.

Let's assume that the number of adult tickets sold is represented by "a," and the number of child tickets sold is represented by "c."

According to the given information, we know that the total number of tickets sold is 700. Therefore, we have our first equation:

a + c = 700

We are also given that the total revenue received from the ticket sales is $2900. The price of an adult ticket is $5, and the price of a child ticket is $3. Therefore, the second equation can be written as:

5a + 3c = 2900

Now we have a system of two equations with two variables. We can solve this system to find the values of "a" and "c."

One way to solve this system is by substitution. From the first equation, we can express "a" in terms of "c" by subtracting "c" from both sides:

a = 700 - c

We can then substitute this expression for "a" into the second equation:

5(700 - c) + 3c = 2900

Simplifying this equation will give us the value of "c." Let's solve it step by step:

3500 - 5c + 3c = 2900
3500 - 2c = 2900
-2c = 2900 - 3500
-2c = -600
c = -600 / -2
c = 300

Now that we have the value of "c," we can substitute it back into the first equation to find the value of "a":

a + 300 = 700
a = 700 - 300
a = 400

Therefore, 400 adult tickets and 300 child tickets were sold.

number of adult tickets --- x

number of children tickets ---- 700-x

5x + 3(700-x) = 2900

carry on ....