# 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 seni

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?

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4 weeks 2023-01-07T20:25:13+00:00 1 Answer 0 views 0

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.