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?
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.
