Question

How do I solve this word problem?

Answer 1

Answer:

• 280 student tickets
• 520 adult tickets

Step-by-step explanation:

You may recognize that you are given two relationships between two unknowns. You can write equations for that.

You are asked for numbers of adult tickets and of student tickets. It often works well to let the values you're asked for be represented by variables. We can choose "a" for the number of adult tickets, and "s" for the number of student tickets. Then the problem statement tells us the relationships ...

  a + s = 800 . . . . . . 800 tickets were sold

  12.50a + 7.50s = 8600 . . . . . . . revenue from sales was 8600

(You are supposed to know that the revenue from selling "a" adult tickets is found by multiplying the ticket price by the number of tickets: 12.50a.)

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You can solve these two equations any number of ways. One way is to do it by elimination. We can multiply the first equation by 12.50 and subtract the second equation:

  12.50(a +s) -(12.50a +7.50s) = 12.50(800) -(8600)

  5s = 1400 . . . . simplify. (The "a" variable has been eliminated.)

  s = 280 . . . . . . divide by 5

Then the number of adult tickets can be found from the first equation:

  a + 280 = 800

  a = 520

280 student tickets and 520 adult tickets were sold.