1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sergeeva-Olga [200]
2 years ago
13

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 m

any 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?
Mathematics
1 answer:
Dmitry [639]2 years ago
8 0

Answer:

The minimum possible initial amount of fish:52

Step-by-step explanation:

Let's start by saying that

x = is the initial number of fishes

John:

When John arrives:

  • he throws away one fish from the bunch

x-1

  • divides the remaining fish into three.

\dfrac{x-1}{3} + \dfrac{x-1}{3} + \dfrac{x-1}{3}

  • takes a third for himself.

\dfrac{x-1}{3} + \dfrac{x-1}{3}

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

\text{John}=\dfrac{x-1}{3} + \dfrac{x-1}{3}

and simplify it!

\text{John}=\dfrac{2x}{3} - \dfrac{2}{3}

When Joe arrives:

  • he throws away one fish from the remaining bunch

\text{John} -1

  • divides the remaining fish into three

\dfrac{\text{John} -1}{3} + \dfrac{\text{John} -1}{3} + \dfrac{\text{John} -1}{3}

  • takes a third for himself.

\dfrac{\text{John} -1}{3}+ \dfrac{\text{John} -1}{3}

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

\text{Joe}=\dfrac{\text{John} -1}{3}+ \dfrac{\text{John} -1}{3}

and simiplify it

\text{Joe}=\dfrac{2}{3}(\text{John}-1)

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

\text{Joe}=\dfrac{2}{3}\left(\dfrac{2x}{3} - \dfrac{2}{3}-1\right)

\text{Joe}=\dfrac{4x}{9} - \dfrac{10}{9}

When James arrives:

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

\text{James}=\dfrac{\text{Joe} -1}{3}+ \dfrac{\text{Joe} -1}{3}

\text{James}=\dfrac{2}{3}\left(\dfrac{4x}{9} - \dfrac{10}{9}-1\right)

\text{James}=\dfrac{8x}{27} - \dfrac{38}{27}

This is the last remaining pile of fish.

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

Whatever the last remaining pile was (let's say n), a third is taken away by James. the remaining bunch would be \frac{n}{3}+\frac{n}{3}

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:

\dfrac{n}{3}+\dfrac{n}{3}=\dfrac{8x}{27} - \dfrac{38}{27}

\dfrac{2n}{3}=\dfrac{8x}{27} - \dfrac{38}{27}

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)

14=\dfrac{8x}{27} - \dfrac{38}{27}

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!

14=\dfrac{8x}{27} - \dfrac{38}{27}

x=52

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

You might be interested in
Please help asap &lt;3333333
SOVA2 [1]

Answer:

1: 75 degrees

2: 112 degrees

3: 125 degrees

4: 67 degrees

Step-by-step explanation:

4 0
2 years ago
Which number line shows the solution set for 1h-21 = 4?
Dafna11 [192]

Answer: Option 2

Step-by-step explanation:

|h-2|=4\\\\h-2=\pm 4\\\\h=-2, 6

8 0
2 years ago
Shown below is a blueprint for a rectangular kennel at a pet hotel.
yulyashka [42]

Answer:

The total length of fencing needed to enclose the kennel 74 feet.

Step-by-step explanation:

Given:

The blueprint of the rectangular kennel shows one side is 23 feet and another side is 14 feet.

As it is a rectangular shape, let the two sides be the length and the breadth of the rectangular kennel. i.e

length = L = 23\ feet\\breadth = B = 14\ feet\\

To find:

Total length of fencing needed is to enclose the kennel. i.e

Perimeter of a rectangular kennel = ?

Solution:

we have the formula for perimeter of a rectangle as giving below.

\textrm{perimeter of rectangle} = 2(length + breadth) \\\textrm{total length of fencing} = 2( L+B)\\ \textrm{substituting the values of length and breadth we get}\\ \textrm{total length of fencing} = 2(23+14)\\=2\times37\\= 74\ feet

Therefore,the total length of fencing needed to enclose the kennel 74 feet.

8 0
3 years ago
Devaughn's age is two times Sydney's age. The sum of their ages is 18. What is Sydney's age?
emmainna [20.7K]

Answer:

Sydney's Age is 6

Step-by-step explanation:

6 x 2 = 12

12 + 6 = 18

8 0
2 years ago
Read 2 more answers
In a recent study, volunteers who had 8 hours of sleep were three times more likely to answer questions correctly on a math test
kumpel [21]

Answer:

(c) the sample is amount of sleep the volunteers got in the study.

Step-by-step explanation:

sample: this is a small part that is intending to show what a big part is all about.

volunteer: a person who does something willingly.

6 0
3 years ago
Other questions:
  • Which of the following is an advantage of an observational study over a sample survey? A)Observational studies are not dependent
    12·1 answer
  • دریافت رمزدوم کارت عابربانک ملت بهاره تبری
    5·1 answer
  • MATH<br><br>ANSWER and I will give you brainiliest ​​
    6·2 answers
  • Johnny spend 1/7 of his income on Food, 1/10 of his income on gas, and 3/8 of his income on rent. What percentage of his income
    9·1 answer
  • A classroom had 35 glue sticks. If the ratio of glue sticks to glue bottles was 5:2, how many glue bottles did the classroom hav
    8·2 answers
  • Which of the following inequalities represents a number y that is less than 4 but greater than -1
    12·1 answer
  • Do you have any equal/opposite terms or variables? <br> x+3y=7 and 2x-4y=-6<br> yes<br> no
    5·1 answer
  • At a small private college 9 / 20 of the students are female if there are 2160 female students how many male students
    11·1 answer
  • Decribe the counter clockwise rotation that maps angles
    7·1 answer
  • The point M(-6, -4) is translated 2 units right. What are the coordinates of the resulting point, M'?​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!