17N.2.AHL.TZ0.H_1

pestleMathematicsAAHLPaper 217N· ahl-1-16-solution-of-systems-of-linear-equationssource ↗

Boxes of mixed fruit are on sale at a local supermarket.

Box A contains 2 bananas, 3 kiwifruit and 4 melons, and costs $6.58.

Box B contains 5 bananas, 2 kiwifruit and 8 melons and costs $12.32.

Box C contains 5 bananas and 4 kiwifruit and costs $3.00.

Find the cost of each type of fruit.

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

let $b$ be the cost of one banana, $k$ the cost of one kiwifruit, and $m$ the cost of one melon

attempt to set up three linear equations (M1)

$2b + 3k + 4m = 658$

$5b + 2k + 8m = 1232$

$5b + 4k = 300$ (A1)

attempt to solve three simultaneous equations (M1)

$b = 36,{\text{ }}k = 30,{\text{ }}m = 124$

banana costs ($)0.36, kiwifruit costs ($)0.30, melon costs ($)1.24 A1

[4 marks]

Examiners’ report

[N/A]