Math

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Jim Kim Mim and Tim all went fishing. They each caught one fish. They measured each fish to the nearest inch and weighed them to the nearest pound. When they lined the fish up end to end they stretched from one edge of the 6-foot-long table to the other. The four fish weighed a total of 20 pounds. Tim's fish was the longest and one of only two fish that were of equal weight. Jim's fish was one inch shorter than Tim's and one inch longer than Kim's. Kim's fish was the shortest and lightest. It weighed a full two lbs less than Mim's. The weight of Jim's and Tim's fish combined was the same as Mim's and Kim's two fish combined. The shortest fish was 1 foot 5 inches long. What was the weight (in pounds) and length (in inches) of each person's fish(?)
I can't figure this one out. Please help!

  • Math -

    Let the lengths in inches be represented by the uppercase initials, J,K,M,T, and the weights in pounds by the lowercase initials, j,k,m,t.

    J+K+M+T=72 ....(1)
    j+k+m+t=20 ....(2)

    T-J=1 ....(3)
    J-K=1 ....(4)

    m-k=2 ....(5)
    j+t=m+k ...(6)
    use(2) to conlude that
    j+t=m+k=10 ....(6A)

    From m-k=2 and m+k=2, calculate m and k.

    "Tim's fish was the longest and one of only two fish that were of equal weight." =>
    t≠m, otherwise j=k.
    Likewise, t≠k, otherwise j=m.

    Therefore t=j=5

    The shortest fish was 1 foot 5 inches (17") long. =>
    T+J+K=17"+18"+19"=54
    M=72-54=18

    Read and understand the above carefully, solve for all the variables, and post if you have questions.

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