Gabriellas school is selling tickets to a fall musical. On the dirst day of ticket sales the school sold 10 senior citizen tickets and 14 student tickets for a total of $212. Tje school took in$232 on the second day by selling 12 senior citizen tickets and 14 student tickets. What is the price each of one senior citizen tickets and one student ticket?
A senior ticket costs $10, while a student ticket costs $8. You can solve this system of equations by the elimination method.
We can use x as the variable for the senior tickets, and y as the variable for the student tickets and represent it with these equations: 10x+12y=212 and 12x+14y=232
Next, multiply each entire equation by a variable so they can eliminate each other. I used 12 and -10 here so it would be 120x-120x to eliminate that variable. 12(10x+14y=212) and -10(12x+14y=232)
Our new equations are: (120x +168y= 2544) and (-120x-140y=-2320)
You can then subtract one of the equations from the other leaving you with 28y=224 and solve it for y to get 8. So the price of a student ticket is 8.
Pick any of the original equations and by replacing y with 8, you can solve to find x. (X is the variable we assigned for senior tickets) 10x+14(8)=212 10x+112=212 10x=212-112 10x= 100 1x=10
