Approximately 2000 tickets are being sold for a car show next Saturday. The cost of a ticket for an adult is $4 and for a child, it’s $2. The total amount collected on Friday was $6400. Find the number of adult tickets and child tickets sold on Friday?

number of adult tickets ---- x

number of children tickets -- 2000-x

solve:
4x + 2(2000-x) = 6400

solve the value of x into my definitions

2800

To find the number of adult and child tickets sold on Friday, we can set up a system of equations based on the given information.

Let's assume the number of adult tickets sold on Friday is "x" and the number of child tickets sold on Friday is "y".

We are given that the total number of tickets sold on Friday is 2000. So, we can write the first equation as:

x + y = 2000

We are also given that the total amount collected on Friday was $6400. The cost of an adult ticket is $4, so the total amount collected from the sale of adult tickets is 4x. Similarly, the cost of a child ticket is $2, so the total amount collected from the sale of child tickets is 2y. This leads us to the second equation:

4x + 2y = 6400

Now we have a system of equations:

x + y = 2000
4x + 2y = 6400

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the method of substitution to solve this system:

From the first equation, we can express y in terms of x:

y = 2000 - x

Now, substitute this expression for y in the second equation:

4x + 2(2000 - x) = 6400

Simplify the equation:

4x + 4000 - 2x = 6400

Combine like terms:

2x + 4000 = 6400

Subtract 4000 from both sides:

2x = 2400

Divide both sides by 2:

x = 1200

Now substitute the value of x back into the first equation to find y:

1200 + y = 2000

Subtract 1200 from both sides:

y = 800

Therefore, the number of adult tickets sold on Friday is 1200, and the number of child tickets sold on Friday is 800.