Question

An office manager booked 55 airline tickets. He booked 6 more tickets on Airline A than Airline B. On Airline C, he booked 5 more than twice as many tickets as on Airline B. How many tickets did he book on each Airline?

Answer 1

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Answer:

• A: 17
• B: 11
• C: 27

Explanation:

If we let a, b, c represent tickets booked on airlines A, B, C, respectively, then we have ...

a + b + c = 55

a - b = 6

-2b + c = 5

Using the last two equations to write expressions for a and c, we have ...

a = b +6

c = 5 +2b

These can be substituted into the first equation to give ...

(b +6) +b +(5 +2b) = 55

4b +11 = 55

4b = 44

b = 11

a = b+6 = 17

c = 5 +2b = 27

He booked 17 tickets on Airline A, 11 tickets on Airline B, and 27 tickets on Airline C.