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Case study·Hard exam skill (4/5)·No calculatorNeeds mentor review

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

At a school fair, adult, student, and child tickets are sold. Let x,y,zx,y,z be the numbers of adult, student, and child tickets. The data gives x+y+z=100, 100x+50y+20z=6100, x−y=10.x+y+z=100,\ 100x+50y+20z=6100,\ x-y=10.
Total: 4 marks

(a) Write the system in matrix form. (1 mark)

(b) State why the system has a unique solution if the coefficient determinant is −110-110. (1 mark)

(c) Find x,y,zx,y,z. (2 marks)

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cbse-math-12.u2.t2-7.case.005

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