Question

The office manager booked 61 airline tickets. He booked 7 more tickets on airline A than C. He booked 4 more than three × as many on airline B. How many did he book on each airline?

A. Airline A: 24, Airline B: 17, Airline C: 20
B. Airline A: 21, Airline B: 20, Airline C: 20
C. Airline A: 22, Airline B: 23, Airline C: 16
D. Airline A: 20, Airline B: 13, Airline C: 21

Answer 1

Based on the given equations, the correct numbers for the airline tickets booked do not match any of the provided answer choices. The equations yield A = 17, B = 34, and C = 10, which add up to 61 tickets, but there is no corresponding option.

Step-by-step explanation:

The office manager booked a total of 61 airline tickets. We have three unknowns: tickets for Airline A (A), Airline B (B), and Airline C (C). We set up equations based on the information given:

1. A = C + 7
2. B = 3C + 4
3. A + B + C = 61

You need to substitute A and B with expressions in terms of C, based on the first two equations. Doing so gives us two new equations:

1. A = C + 7
2. B = 3(C) + 4
3. (C + 7) + (3C + 4) + C = 61

Combining like terms and solving this equation for C:

5C + 11 = 61,

C = 50/5,

C = 10.

Substituting C back into the equations for A and B:

A = 10 + 7,

A = 17,

B = 3(10) + 4,

B = 34.

However, when plugging the values back into the third equation, you find that the sum of A, B, and C (17 + 34 + 10) is 61, which does not add up correctly to the 61 airline tickets that were booked. Hence, there seems to be an inconsistency with the options provided. No provided options, A through D, match these calculated amounts - this looks like a problem that requires revisiting the initial question or options.