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