| Date | November 2016 | Marks available | 2 | Reference code | 16N.1.sl.TZ0.8 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 8 | Adapted from | N/A |
Question
Passengers of Flyaway Airlines can purchase tickets for either Business Class or Economy Class.
On one particular flight there were 154 passengers.
Let \(x\) be the number of Business Class passengers and \(y\) be the number of Economy Class passengers on this flight.
On this flight, the cost of a ticket for each Business Class passenger was 320 euros and the cost of a ticket for each Economy Class passenger was 85 euros. The total amount that Flyaway Airlines received for these tickets was \({\text{14}}\,{\text{970 euros}}\).
The airline’s finance officer wrote down the total amount received by the airline for these tickets as \({\text{14}}\,{\text{270 euros}}\).
Use the above information to write down an equation in \(x\) and \(y\).
Use the information about the cost of tickets to write down a second equation in \(x\) and \(y\).
Find the value of \(x\) and the value of \(y\).
Find the percentage error.
Markscheme
\(x + y = 154\) (A1) (C1)
[1 mark]
\(320x + 85y = 14\,970\) (A1) (C1)
[1 mark]
\(x = 8,{\text{ }}y = 146\) (A1)(ft)(A1)(ft) (C2)
Note: Follow through from parts (a) and (b) irrespective of working seen, but only if both values are positive integers.
Award (M1)(A0) for a reasonable attempt to solve simultaneous equations algebraically, leading to at least one incorrect or missing value.
[2 marks]
\(\left| {\frac{{14270 - 14970}}{{14970}}} \right| \times {\text{ }}100\) (M1)
Note: Award (M1) for correct substitution into percentage error formula.
\( = 4.68(\% ){\text{ }}(4.67601 \ldots ){\text{ }}\) (A1) (C2)
[2 marks]
