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3 November, 03:37

A fisherman caught 15kg fishnon Monday and 23kg on Tuesday. on Tuesday there were twice as many fish as on Monday, but their average mass was, 1|8 kg less. how many fish did the Fisherman catch on Monday?

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  1. 3 November, 06:57
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    28 fish were caught on Monday.

    Let's create some equations for this problem. The following variables will be used

    Fm = Fish caught on Monday

    Mm = Average mass of fish caught on Monday

    Ft = Fish caught on Tuesday

    Mt = Average mass of fish caught on Tuesday

    So we have the following equations:

    15 = Fm * Mm

    23 = Ft * Mt

    Ft = 2 * Fm

    Mt = Mm - 0.125

    Let's substitute the equations for Ft and Mt into the equation for fish caught on Tuesday

    23 = Ft * Mt

    23 = 2 * Fm (Mm - 0.125)

    23 = 2 * Fm * Mm - 2 * Fm * 0.125

    23 = 2 * Fm * Mm - 0.25 * Fm

    Now we know from Monday that Fm*Mm is 15, so let's substitute that into the equation and solve for Fm

    23 = 2 * Fm * Mm - 0.25 * Fm

    23 = 2 * 15 - 0.25 * Fm

    23 = 30 - 0.25 * Fm

    -7 = - 0.25 * Fm

    28 = Fm

    We now know that 28 fish were caught on Monday.

    Let's verify that everything makes sense.

    Fm = 28

    Mm = 15 / 28

    Ft = 2 * Fm = 2 * 28 = 56

    Mt = 23 / 56

    Mm - Mt = 1/8

    15/28 - 23/56 = 1/8

    30/56 - 23/56 = 1/8

    7/56 = 1/8

    1/8 = 1/8

    And we get a true statement. So the calculated number of fish caught on Monday is correct.
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