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Date	May 2022	Marks available	2	Reference code	22M.1.SL.TZ1.5
Level	Standard Level	Paper	Paper 1	Time zone	Time zone 1
Command term	Find	Question number	5	Adapted from	N/A

Question

The ticket prices for a concert are shown in the following table.

A total of $600$ tickets were sold.
The total amount of money from ticket sales was $$ 7816$ .
There were twice as many adult tickets sold as child tickets.

Let the number of adult tickets sold be $x$ , the number of child tickets sold be $y$ , and the number of student tickets sold be $z$ .

Write down three equations that express the information given above.

[3]

Find the number of each type of ticket sold.

[2]

Markscheme

$x + y + z = 600$ A1

$15 x + 10 y + 12 z = 7816$ A1

$x = 2 y$ A1

Note: Condone other labelling if clear, e.g. $a$ (adult), $c$ (child) and $s$ (student). Accept equivalent, distinct equations e.g. $2 y + y + z = 600$ .

[3 marks]

$x = 308, y = 154, z = 138$ A1A1

Note: Award A1 for all three correct values seen, A1 for correctly labelled as $x, y$ or $z$ .
Accept answers written in words: e.g. $308$ adult tickets.

[2 marks]

Examiners report

Many candidates had at least two of the three equations written down correctly. The interpretation of the phrase “twice as many adult tickets sold as child tickets” was enigmatic. Consequently, $2 x = y$ was a popular but erroneous answer.

Too many candidates spent considerable time attempting to solve three equations with three unknowns by hand with pages of working rather than using their GDC.

Syllabus sections

Topic 2—Functions » SL 2.6—Modelling skills

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21N.2.SL.TZ0.3f.ii:
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22M.1.SL.TZ1.5a:
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22M.1.SL.TZ2.9c:
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22M.1.SL.TZ1.11a:
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EXM.3.AHL.TZ0.9f.i:
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EXM.3.AHL.TZ0.9f.iii:
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EXM.2.SL.TZ0.3d.i:
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maximum value of $h$ .
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Calculate the angle, in degrees, that the blade $[BC]$ turns through in one second.
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Find the time, in seconds, that point $C$ is above a height of $100 m$ , during each complete rotation.
21N.2.AHL.TZ0.2f:
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Topic 1—Number and algebra » SL 1.8—Use of technology to solve systems of linear equations and polynomial equations

Topic 1—Number and algebra

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