The school that Willie goes to is selling tickets to a school performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 12 student tickets for a total of $213. The school took in $85 on the second day by selling 5 senior citizen tickets and 2 student tickets. What is the price each of one senior citizen and one student ticket?

Question

radar · Answer

Let x be the price of senior tickets
Let y be the price of student tickets

Day 1. 3x+12y=$213.00
Day 2. 5x+2y=$85.00   Take day 2 equation and multiply all by 6 so that
Day 2. 30x+12y=$510.00    now subtract Day 1 equation
Day 1 -3x-12y=-213.00  getting
          27x  = 297  divide by 27 getting x=$11.00
Senior tickets cost $11.00    substitute in day 1 and find y the students ticket cost
3(11.00)+12y=213.00
33.00 +12y =213.00    subtract 33 from both sides
12y=213.00-33=180.00    divide by 12
y=$15.00 Students ticket cost $15.00 each.

radar · Answer

Day 2 equation was multiplied by 6 for the sole reason of getting the y variable to equal 12, so when subtracted from day 1 equation the y value would drop out leaving only x so it could be solved.