a total of 517 tickets were sold for the school play. they were either adult tickets or student tickets. there were 67 more student tickets sold than adult tickets. how many adult tickets were sold?

  225 adult tickets were sold

Step-by-step explanation:

You are asked to find the number of adult tickets sold. It is convenient to let a variable represent that quantity. We can call it "a" to remind us it is the number of adult tickets (not student tickets).

The number of student tickets is 67 more, so can be represented by (a+67). The total number of tickets sold is the sum of the numbers of adult tickets and student tickets:

  (a) + (a+67) = 517

  2a + 67 = 517 . . . . . collect terms

  2a = 450 . . . . . . . . . subtract 67

  a = 225 . . . . . . . . . . divide by 2

There were 225 adult tickets sold.

Check

The number of student tickets sold is ...

  a+67 = 225 +67 = 292

And the total number of tickets sold is ...

  225 + 292 = 517 . . . . . answer checks OK

step-by-step explanation: