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

Answer:

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