Mookie, Gandalf, and O’Malley are selling tickets to a play. Gandalf sold five less than three times the number of tickets Mookie sold. O’Malley sold one more than seven times the number of tickets Mookie sold. The number of tickets O’Malley sold is four more than twice the number of tickets that Mookie and Gandalf sold together. How many tickets did they sell in total?

9514 1404 393

  73

Step-by-step explanation:

Let m, g, o represent the numbers sold by Mookie, Gandalf, and O'Malley, respectively. Then the relations between these values are ...

  g = 3m -5

  o = 7m +1

  o = 4 +2(m +g)

Equating expressions for o, we have ...

  7m +1 = 4 +2(m +g)

Substituting for g, we have ...

  7m +1 = 4 +2(m +(3m -5))

  7m +1 = 8m -6

  7 = m . . . . . . . . add 6-7m

  g = 3·7 -5 = 16

  o = 7·7 +1 = 50

The number sold in total is ...

  m + g + o = 7 +16 +50 = 73

They sold 73 tickets in total.

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