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March 25, 2017

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Jim bought some chocolates and gave half of it to Ken.Ken bought sweets and gave half of it to Jim.Jim ate 12 sweets and Ken ate 18 chocolates.The ratio of Jim's sweets to chocolate became 1:7 and the ratio of ken's sweets to chocolates became 1:4.How many sweets did Ken buy?

  • Math - ,

    Ken buys 68 sweets.

  • Math - ,

    make a chart:
    ....Jim...Ken
    c choc's .. s sweets
    after exchange:
    (1/2)s + (1/2)c ... (1/2)s + (1/2)c
    after eating:
    Jim eats 12 sweets , so amount left:
    (1/2)s - 12 sweets and (1/2)c choc's
    but that ratio is 1:7
    so [(1/2)s - 12]/[(1/2)c] = 1/7
    (s - 24)/c = 1/7
    c = 7s - 168 #1

    Ken eats 18 choc's, so amount left"
    (1/2)s + (1/2)s - 18
    but that ratio is 1:4
    so [(1/2)s]/[(1/2)c - 18] = 1/4
    s/(c-36) = 1/4
    4s = c-36
    c = 4s - 36 #2

    equate #1 and #2 and solve for s
    7s-168 = 4s+36
    s = 68
    back in #1 I get
    c = 308

    check:
    Jim : 68 sweets, Ken : 308 choc's
    after exchange:
    Jim has 34 sweets, 154 chocs
    Ken has 34 sweets, 154 chocs, they have the same
    after eating as stated above
    Jim has 22 sweets, 154 chocs --> ratio = 22:154 = 1:7
    Ken has 34 sweets, 136 choc's --> ratio = 34:136 = 1:4

    checks!!!

  • Math - ,

    Thanks so much Reiny and Ajay Sir

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