Question

You are selling tickets to a concert. Student tickets cost $5 and adult cost $7. You sell 45 tickets and collect $265. How many of each type did you sell?

Answer 1

See a solution process below:

• 25 Adult Tickets were sold
• 20 Student Tickets were sold

Explanation:

First, let's call:

• The number of Adult Tickets sold: `a`
• The number of Student Tickets sold: `s`

We can now write two equations from the information in the problem:

• Equation 1: `a + s = 45`
• Equation 2: `$7a + $5s = $265`

Step 1) Solve the first equation for `a`:

`a + s - color(red)(s) = 45 - color(red)(s)`

`a + 0 = 45 - s`

`a = 45 - s`

Step 2) Substitute `(45 - s)` for `a` in the second equation and solve for `s`:

`$7a + $5s = $265` becomes:

`$7(45 - s) + $5s = $265`

`($7 * 45) - ($7 * s) + $5s = $265`

`$315 - $7s + $5s = $265`

`$315 + (-$7 + $5)s = $265`

`$315 - $2s = $265`

`$315 - color(red)($315) - $2s = $265 - color(red)($315)`

`0 - $2s = -$50`

`-$2s = -$50`

`(-$2s)/(color(red)(-$2)) = (-$50)/(color(red)(-$2))`

`(color(red)(cancel(color(black)(-$2)))s)/cancel(color(red)(-$2)) = 25`

`s = 25`

Step 3) Substitute `25` for `s` in the solution to the first equation at the end of Step 1 and calculate `a`:

`a = 45 - s` becomes:

`a = 45 - 25`

`a = 20`

The Solution Is:

• 20 Adult Tickets were sold
• 25 Student Tickets were sold