Answer:
To solve a system of equations word problem, you need to follow these steps:
Find the key information in the word problem that can help you define the variables.
Define two variables: x and y
Write two equations.
Use the elimination method or the substitution method for solving systems of equations.
Check the solution by substituting the ordered pair into the original equations.
For this problem, you can define x as the number of adult tickets and y as the number of student tickets. Then, you can write two equations based on the information given:
x - y = 15 (She sells 15 fewer student tickets than adult tickets)
8x + 5y = 315 (Adult tickets are $8 each and student tickets are $5 each, and the total sales are $315)
You can use either the elimination method or the substitution method to solve this system of equations. For example, using the substitution method, you can solve for y in the first equation and then substitute it into the second equation:
y = x - 15
8x + 5(x - 15) = 315
13x - 75 = 315
13x = 390
x = 30
Then, you can find y by plugging x into the first equation:
y = 30 - 15
y = 15
You can check the solution by substituting x and y into the original equations and see if they are true:
30 - 15 = 15 (True)
8(30) + 5(15) = 315 (True)
Therefore, the solution is x = 30 and y = 15, which means she sells 30 adult tickets and 15 student tickets.
The equation that would give you the solution if t represents the number of tickets is:
8t + 5(t - 15) = 315
Explanation: