The school stefan is going to is selling tickets to a choral proformance. on the first day of ticket sales the school sold 3 senior citizen tickets and one child ticket for the price of $38. the school took in $52 on the second day by selling 3 senior citizen tickets and two childrens tickets . find the price of a senior citizen ticket and the price of a child ticket

To solve this problem, you must create and solve a system of equations. Let one child ticket be x, and one senior citizen ticket be y. The equations are as follows.

38 = x + 3y
52 = 2x + 3y

It seems the elimination method of solving would be most efficient in this case. To cancel out y-terms, multiply the bottom equation by -3 to negate it.

-1(52 = 2x + 3y)
-52 = -2x - 3y

Now, add the equations together.

   38 = x + 3y
  -52 = -2x - 3y
+
  -14 = -x - 0
   14 = x

The cost for one child ticket is $14 dollars. We still need to find the cost of one senior citizen ticket. To do that, substitute 14 for x into either of the original equations and solve.

38 = x + 3y
38 = 14 + 3y
24 = 3y
8 = y

The cost of one senior citizen ticket is $8. There is one more step - substitute both tickets costs into each original equation to check work.

38 = x + 3y
38 = 14 + 3(8)
38 = 14 + 24
38 = 38

52 = 2x + 3y
52 = 2(14) + 3(8)
52 = 28 + 24
52 = 52

The price of a senior citizen ticket is eight dollars and the price of a child ticket is fourteen dollars.