2000 tickets were sold in an exhibition on Saturday. The cost of a ticket for an adult is $4 and for a child is $2. The total amount collected on Saturday was $6400. Find the number of adult tickets and child tickets sold on Saturday.

Let x = # of adult tickets sold (at $4.00 each)

Let y = # of child tickets sold (at $2.00 each)

We can take the above information, along with the 2000 tickets sold and the $6,400 collected, to get the following two math statements:

x + y = 2000 (Total unknown number of $4.00 + total unknown number of $2.00 tickets, equals a total of 2,000 tickets sold

4x + 2y = 6400 ($4.00 * unknown number of $4.00 tickets + $2.00 * unknown number of $2.00 tickets, equals the total of $6,400 collected in ticket sales

So, write these as:

x + y = 2000

4x + 2y = 6400

Take the first equation: Turn it into a y = statement, by subtracting 'x' from both sides, to get:

y = 2000 - x

Next, go to the 2nd equation. Where you see the 'y', substitute the y-value in its place: '2000 - x'

This gives you:

4x + 2 (2000 - x) = 6400

This then gives us: 4x + 4000 - 2x = 6400

Collect like terms to get:

2x + 4000 = 6400

Subtract 4000 from both sides to get:

2x = 2400

Next, divide both sides by 2, to get x = 1200

We now know that there were 1,200 adult ($4.00) tickets sold; put this information back into the original equation:

1200 + y = 2000

Next, subtract 1200 from both sides, so that we can solve for y; which is:

y = 800

Next, check our work, by substituting back into the two original equations:

1200 + 800 = 2000 [Check]

4 * 1200 + 2 * 800 = 4800 + 1600 + 6400 [Check]

So: 1,200 tickets sold at $4.00 each; and 800 tickets sold at $2.00 each, final and correct answer.