John, joe, and james go fishing. at the end of the day, john comes to collect his third of the fish. however, there is one too many fish to make equal thirds, so john throws it out, takes his third and leaves. joe comes to get his fish without realizing john has already taken his third. he notices that there is one too many fish to make equal thirds, so he throws one out, takes his fish and leaves. james notices that there is one too many fish to make equal thirds, so he throws one out, takes his fish and leaves. assuming no fish are divided into pieces, what is the minimum possible number of fish before john threw out the first fish?

The minimum possible initial amount of fish:

Step-by-step explanation:

Let's start by saying that

= is the initial number of fishes

John:

When John arrives:

the remaining fish are expressed by the above expression. Let's call it John

and simplify it!

When Joe arrives:

the remaining fish are expressed by the above expression. Let's call it Joe

and simiplify it

since we've already expressed John in terms of x, we express the above expression in terms of x as well.

When James arrives:

We're gonna do this one quickly, since its the same process all over again

This is the last remaining pile of fish.

We know that no fish was divided, so the remaining number cannot be a decimal number. We also know that this last pile was a multiple of 3 before a third was taken away by James.

Whatever the last remaining pile was (let's say ), a third is taken away by James. the remaining bunch would be

hence we've expressed the last pile in terms of n as well.  Since the above 'James' equation and this 'n' equation represent the same thing, we can equate them:

L.H.S must be a Whole Number value and this can be found through trial and error. (Just check at which value of n does 2n/3 give a non-decimal value) (We've also established from before that n is a multiple a of 3, so only use values that are in the table of 3, e.g 3,6,9,12,..

at n = 21, we'll see that 2n/3 is a whole number = 14. (and since this is the value of n to give a whole number answer of 2n/3 we can safely say this is the least possible amount remaining in the pile)

by solving this equation we'll have the value of x, which as we established at the start is the number of initial amount of fish!

This is minimum possible amount of fish before John threw out the first fish

cbnygjdyj

step-by-step explanation:

which would be true for stem changing verbs?

they have a consistent spelling change in the stem of the verb.

what is different about the verb “venir” as compared to other stem-changing verbs?

only the third person forms have a stem change.

which of the following could not be considered a “stem-changing” verb?

querer

which of the following would not be condsidered an event?

desfile

what word could be used in response to the following?

¿qué quieres comprar?

quero

what word could be used in response to the following?

¿dónde uds. pueden ir?

vamos  

ellos ir al centro comercial.

yo comprar un vestido.

pedimos

dónde tú?

dormes

step-by-step explanation: