MATHS

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24 1c coins are set out in a row on a table
Then every 2nd coin is replaced by a 2c coin
every 3rd coin is replaced by a 5c coin
every 4th coin is replaced by a 10c coin
every 5th coin is replaced by a 20c coin
every 6th coin is replaced by a 50c coin and every 7th coin is replaced by a $1coin
After all the exchanges have been carried out, what is the total amount left on the table?

The answer is $6.30

  • MATHS -

    all multiples of 7 are $1
    7, 14, 21 ------- $3.00

    all multiples of 6 are .50
    6,12,18,24,------- 4(.50) = $2.00

    all multiples of 5 are .20
    5,10,15,20 ---- 4(.20) = $.80

    all multiples of 4 are .10
    4,8,12,16,20,24
    but the 12, 20 and 24 have been changed, so
    only the 4,8, and 16 contain .10 ---- $.30

    only multiples of 3 that have not been changed are
    3 and 9 at .05 ------- $ .10

    only the 2 and 11 of all the evens is still at .02
    ----------- $.04

    leaving the remaining
    1, 11, 13, 17, 19, and 23 to still have their .01
    -------- .06

    3 + 2 + .8 + .3 + .1 + .04 + .06
    = 6.30

    you are correct

  • MATHS -

    This problem is like the "Locker Problem" from "Prime Time, Connections 3."

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