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
Accepted Solution
A:
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.