Write down an equation in \(x\) and \(y\) .

The cost of an adult ticket was \(12\) Australian dollars (AUD). The cost of a child ticket was \(5\) Australian dollars (AUD).

Find the total cost for a family of 2 adults and 3 children.

The total cost of tickets sold for the sports match was \(108800{\text{ AUD}}\).

Write down a second equation in \(x\) and \(y\) .

Write down the value of \(x\) and the value of \(y\) .

\(x + y = 10000\)     (A1)     (C1)

[1 mark]

\(2 \times 12 + 3 \times 5\)     (M1)

\(39{\text{ }}(39.0{\text{, }}39.00)\) (AUD)     (A1)     (C2)

[2 marks]

\(12x + 5y = 108800\)     (A1)     (C1)

[1 mark]

\(x = 8400\), \(y = 1600\)     (A1)(ft)(A1)(ft)     (C2)

Notes: Follow through from their equations. If \(x\) and \(y\) are both incorrect then award (M1) for attempting to solve simultaneous equations.

[2 marks]

The first three marks were obtained by a significant majority of candidates. The second equation in \(x\) and \(y\) proved to be a little more elusive and a popular, but incorrect, answer seen was \(12x + 5y = 10000\) . Where working was seen in part (d), much of it was wrong. Indeed, a popular, but erroneous method, was to make either \(x\) (or \(y\)) the subject using one equation and then back substituting the value found into the same equation. Answers, involving decimals, should have flagged to the candidate that something was going wrong somewhere and another look at the question was required. Algebra is always a discriminator on these papers and centres would be well advised to reinforce concepts in such topics.

The first three marks were obtained by a significant majority of candidates. The second equation in \(x\) and \(y\) proved to be a little more elusive and a popular, but incorrect, answer seen was \(12x + 5y = 10000\) . Where working was seen in part (d), much of it was wrong. Indeed, a popular, but erroneous method, was to make either \(x\) (or \(y\)) the subject using one equation and then back substituting the value found into the same equation. Answers, involving decimals, should have flagged to the candidate that something was going wrong somewhere and another look at the question was required. Algebra is always a discriminator on these papers and centres would be well advised to reinforce concepts in such topics.

The first three marks were obtained by a significant majority of candidates. The second equation in \(x\) and \(y\) proved to be a little more elusive and a popular, but incorrect, answer seen was \(12x + 5y = 10000\) . Where working was seen in part (d), much of it was wrong. Indeed, a popular, but erroneous method, was to make either \(x\) (or \(y\)) the subject using one equation and then back substituting the value found into the same equation. Answers, involving decimals, should have flagged to the candidate that something was going wrong somewhere and another look at the question was required. Algebra is always a discriminator on these papers and centres would be well advised to reinforce concepts in such topics.

The first three marks were obtained by a significant majority of candidates. The second equation in \(x\) and \(y\) proved to be a little more elusive and a popular, but incorrect, answer seen was \(12x + 5y = 10000\) . Where working was seen in part (d), much of it was wrong. Indeed, a popular, but erroneous method, was to make either \(x\) (or \(y\)) the subject using one equation and then back substituting the value found into the same equation. Answers, involving decimals, should have flagged to the candidate that something was going wrong somewhere and another look at the question was required. Algebra is always a discriminator on these papers and centres would be well advised to reinforce concepts in such topics.