solving word problems with systems

Question

The school that Imani goes to is selling tickets to the annual dance competition. On the first day

of ticket sales the school sold 12 senior citizen tickets and 6 student tickets for a total of $252.

The school took in $98 on the second day by selling 6 senior citizen tickets and 1 student ticket.

What is the price each of one senior citizen ticket and one student ticket?

Answer 1

both cost the same, $14 per ticket, for senior citizens or students

12e + 6s = 252

2e +s = 42

2(14)+14 = 28+14 = 42

6e + s = 98

6(14)+14 = 84+14 = 98

12e +2s = 196

subtract last just above from 1st equation

6s -2s = 252-196

4s = 56

s = 56/4 = $14 for a student ticket

e = 98-14)/6 = 84/6 = $14 for a senior ticket

12(14)+6(14) = 18(14) = $252

6(14) +14 = 7(14) = $98

both cost $14 per ticket