Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $50. For one performance, 25 advance tickets and 15 same-day tickets were sold. The total amount paid for the tickets was $900. What was the price of each kind of ticket?Note that the ALEKS graphing calculator can be used to make computations easier.Advanceticket:$Same-dayticket:$ExplanationCheck© 2024 McGraw Hill LLC. All Rights Reserved.Terms of Use|Privacy Center|AccessibilityClears your work.Undoes your last action.
Question
Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is 900. What was the price of each kind of ticket?Note that the ALEKS graphing calculator can be used to make computations easier.Advanceticket:ExplanationCheck© 2024 McGraw Hill LLC. All Rights Reserved.Terms of Use|Privacy Center|AccessibilityClears your work.Undoes your last action.
Solution
To solve this problem, we can use a system of linear equations. Let's denote:
A = cost of an advance ticket S = cost of a same-day ticket
From the problem, we have two equations:
- A + S = 50 (the combined cost of one advance ticket and one same-day ticket is $50)
- 25A + 15S = 900 (25 advance tickets and 15 same-day tickets were sold for a total of $900)
We can solve this system of equations step by step:
Step 1: Solve the first equation for A: A = 50 - S
Step 2: Substitute A from the first equation into the second equation: 25(50 - S) + 15S = 900 1250 - 25S + 15S = 900 10S = 900 - 1250 10S = -350 S = -350 / 10 S = -35
However, the cost of a ticket cannot be negative, so there must be a mistake in the problem statement. The total amount paid for the tickets (50 each ($2000). Please check the problem statement.
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