We appreciate your visit to Gabriella s school is selling tickets to a fall musical On the first day of ticket sales the school sold 10 senior citizen tickets and. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
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
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
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