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.

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]