Question

The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. The school took in$126 the second day by selling 7 senior citizen tickets and 5 student tickets. What is the price each of one senior citizen ticket and one student ticket?

1. The price of one senior citizen ticket is $8 while the price of one student ticket is$14.

### How to solve simultaneous equations:

Forming the sales units and total revenue for each day as simultaneous equations will give:
Day one sales = 4c + 5s = $102 … equation 1 Day two sales = 7c + 5s =$126    … equation 2

### Data and Calculations:

Senior Citizen (c)     Students  (s)  Total Sales
Day one                    4                         5               $102 Day two 7 5$126
Equation 1: 4c + 5s = $102 Equation 2: 7c + 5s =$126
Elimination:
Deducting equation one from equation two will give:
7c + 5s = $126 – 4c + 5s =$102
= 3c = $24 c =$8 ($24/3) Substitution of c in equation one: 4c + 5s =$102
= 4 x $8 + 5s =$102
= $32 + 5s =$102
5s = $102 –$32
5s = $70 s =$14
Check accuracy in equation two:
7c + 5s = $126 = 7 x$8 + 5 x $14 =$126
= $56 +$70 = $126 Thus, the price of one senior citizen ticket is$8 while the price of one student ticket is \$14.