Question

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?

Answer 1

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.