College Algebra

Question

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket (x) and the price of a child ticket (y).

 

Use Gaussian Elimination method to solve

Answer 1

Let s represent the price of a senior ticket and c that of a child. Therefore, the first day can be represented by

3s + c = 38

Solving for c in terms of s gives us

c = 38 - 3s

Plugging that into the expression for the 2nd day

3s + 2c = 52 = 3s + 2(38-3s) = 3s + 76 - 6s = 76-3s

Solving for s

52 = 76 - 3s

52 - 52 + 3s = 76 - 52 - 3s + 3s

3s = 24

s = 8

c = 38 - 3(8) = 38 - 24 = 14

 

Note that in this instance, an easier solution would be to note that the only difference between sales for the two days was that of a single child ticker and $14 more was earned the second day so the price of a child ticket being $14 is quickly determined.