The college that dora attends!

Question

The college that Dora attends is selling tickets to the annual battle of the bands competition. On the first day of ticket sales the college sold 3 student tickets and 3 adult tickets for a total of $69. The school took in $91 on the second day by selling 5 student tickets and 3 adults tickets. Use elimination to solve the system of linear equations and determine the price each student ticket, x and each adult ticket, y. Write your answer as an ordered pair (x,y).

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Answer 1

Let's tackle this problem one piece at a time

On the first day of ticket sales the college sold 3 student tickets and 3 adult tickets for a total of $69

1. To convert this to an equation, let x = value of one student ticket, and let y = value of one adult ticket
2. We know that 3 students times the value of one student ticket plus 3 adults times the value of one adult ticket results in a total value of $69
3. Therefore, it can be stated algebraically that 3*x + 3*y = 69

The school took in $91 on the second day by selling 5 student tickets and 3 adult tickets

1. To convert this to an equation, we will maintain that x = value of one student ticket, and y = value of one adult ticket
2. We have now additionally learned that 5 students times the value of one student ticket plus 3 adults times the value of one adult ticket results in a total value of $91
3. Therefore, it can be stated algebraically that 5*x + 3*y = 91

Use elimination to solve the system of linear equations and determine the value of one student ticket, x and the value of one adult ticket, y

Write your answer as an ordered pair (x,y)

1. To utilize elimination on a system of two linear equations, one or both equations must be multiplied by a constant on both sides such that adding the two resultant equations eliminates one of the variables
2. One possible solution is to multiply our first equation 3x + 3y = 69 by -1 and add it to our second equation
3. [5x + 3y = 91] + [-1(3x + 3y = 69)]
4. [5x + 3y = 91] + [-3x - 3y = -69]
5. (5x + -3x) + (3y + -3y) = (91 + -69)
6. (5x - 3x) + (3y - 3y) = (91 - 69)
7. (2x) + 0 = 22
8. (2x)/2 = 22/2
9. x = 11 —> the value of one student ticket is $11
10. Now, plug our discovered value for the value of one student ticket, x into either of the original equations to solve for the the value of one adult ticket, y
11. 3(11) + 3y = 69
12. 3(11 + y) = 69
13. 3(y + 11)/3 = 69/3
14. y + 11 = 23
15. y + 11 - 11 = 23 - 11
16. y = 12 —> the value of one adult ticket is $12
17. The solution can be expressed in an ordered pair as (11, 12)