# 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? ##### 1 Answer Mar 17, 2018 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 $a$:

$a + s - \textcolor{red}{s} = 45 - \textcolor{red}{s}$

$a + 0 = 45 - s$

$a = 45 - s$

Step 2) Substitute $\left(45 - s\right)$ 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