Question

For a football game. Adult tickets are 8 dollars and student tickets are 5 dollars. The school sells 2570 tickets and makes a total of $19,060.

how many adult ticket were sold

how many student tickets were sold

Answer 1

You don’t know how many adults were there and how many students were there.

But,

$8(adults) + $5(students) = $19060

And,

Adults + Students = 2570

Let A = adults and S = students

8A + 5S = 19060

A + S = 2570

This is called a system of equations. To solve, you need to rearrange both equations to solve for one of the variables, you can pick any. This makes them cancel out so you can focus on 1 variable. After solving, you can plug the solved variable back into any of the given equations and solve for the second one.

S = 19060/5 - 8A/5

S = 3812 - (8A/5)

This is the first equation rearranged to solve for S

Second:

A + S = 2570

S = 2570 - A

Now, equal each other

3812 - (8A/5) = 2570 - A

Solve for A

3812 + A = 2570 + 8A/5

19060 + 5A = 12850 + 8A

19060 - 12850 = 3A

6210 = 3A

2070 = A

There were 2070 adults

Now, plug A back into any of the 2 equations and solve for S

A + S = 2570

2070 + S = 2570

S = 2570 - 2070

S = 500

2070 adult tickets were sold
500 student tickets were sold