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Encik Khabir bought 2 adult tickets and 3 child tickets for a movie and the total cost is RM46. Mr Foo bought an adult ticket and 2 child tickets for the same movie and the total cost was RM27. Find the cost of an adult ticket and the cost of a child ticket.

Mathematics

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Step-by-step solution

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Let AA be the cost of an adult ticket and CC be the cost of a child ticket.

From the problem statement, we can form two linear equations:

Encik Khabir's purchase:

2A+3C=46(1)2A + 3C = 46 \quad (1)

Mr Foo's purchase:

A+2C=27(2)A + 2C = 27 \quad (2)

  1. Multiply equation (2) by 2 to make the coefficients of AA equal.

    2×(A+2C)=2×272 \times (A + 2C) = 2 \times 27 2A+4C=54(3)2A + 4C = 54 \quad (3)

  2. Subtract equation (1) from equation (3) to eliminate AA.

    (2A+4C)−(2A+3C)=54−46(2A + 4C) - (2A + 3C) = 54 - 46 2A+4C−2A−3C=82A + 4C - 2A - 3C = 8 C=8C = 8

  3. Substitute C=8C = 8 into equation (2) to find AA.

    A+2(8)=27A + 2(8) = 27 A+16=27A + 16 = 27 A=27−16A = 27 - 16 A=11A = 11

    The cost of an adult ticket is RM11 and the cost of a child ticket is RM8.

    The cost of an adult ticket is RM11\boxed{\text{RM11}} and the cost of a child ticket is RM8\boxed{\text{RM8}}.

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