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26 December, 12:56

Bob has hats:scarves=4:3. During the day he sells 25 hats. At the end of the day he has hats:scarves=7:9. Work out the number of scarves he has.

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  1. 26 December, 13:09
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    Bob does not sell any scarves. (If he does, there isn't enough information here to solve the problem.)

    Suppose Bob ends the day with 7k hats and 9k scarves, where k is some integer. This is a ratio of 7:9. Bob started the day with 7k+25 hats and 9k scarves. The ratio at the start of the day is

    (7k+25) / 9k = 4/3

    3 (7k+25) = 4 (9k)

    21k+75 = 36k

    75 = 15k

    k = 5.

    So Bob has 9k = 9x5 = 45 scarves.

    Suppose Jake gets £ 1k and Kim gets £ 3k. Kim gets £ 2k more than Jake, so £ 2k = £ 9.

    Lee gets £ 6k = 3x £ 2k = 3x £ 9 = £ 27.

    The co-ordinates of X are

    x = 2 + (2/5) * (12.5-2) = 6.2

    y = 1 + (2/5) * (7.5-1) = 3.6.
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