Math - shepherd John

Question

John is a shepherd and he has 25 sheep, which are kept in four different sheepfolds. In the first sheepfold there are 3 times as many sheep in the second one. In the fourth one there are twice as many sheep as in the third one.

How many sheep are there in each sheepfold?

Can someone help with this. My friends and I have different answers to this. Thank you

Answer 1

A = 3B

D = 2C where A =1st, B=2nd, C= 3rd, D = 4th sheepfold

A + B + C + D = 25

3B +B + C +2C = 25

4B + 3C = 25

either B = 4, C =3 or

B= 1, C =7

if B=4, A =12, C=3 and D=6

ABCD = 12,4,3, 6

or if B=1, C=7

then A=3, D=14

ABCD = 3,1,7, 14

Two possible solutions

either 1st has 12 sheep, 2nd has 4 sheep, 3rd has 3 sheep, 4th has 6 sheep

or 1st has 3 sheep, 2nd has 1 sheep, 3rd has 7 sheep and 4th has 14 sheep

either way they sum to 25

other infinite numbers of solutions all have fractional sheep, and not realistic

Answer 2

John is a shepherd and he has 25 sheep, which are kept in four different sheepfolds. In the first sheepfold there are 3 times as many sheep in the second one. In the fourth one there are twice as many sheep as in the third one.

let x = second sheepfold

3x = first sheepfold

2y = fourth sheepfold

y = third sheepfold

x+3x+y+2y = 25

4x+3y=25

4x=25-3y

x=(25-3y)/4 = second sheepfold

3x = 3(25-3y)/4 = first sheepfold

Solve for y(third sheepfold), and 2y(fourth sheepfold)

Answer 3

Hey Sandra,

So 25 sheep total.

1st sheepfold is 3x

2nd sheepfold is x

3rd sheepfold is y

4th sheepfold is 2y

Since theres no other information about a third relationship (i.e. specified different amounts between 2 and 3), I basically used trial and error and basic reasoning that you cant have half a sheep. I just plugged in a random number for sheephold 4 and worked backwords.

I found that the numbers should be:

sheepfold 1 = 12 sheep, sheepfold 2 = 4 sheep, sheepfold 3 = 3 sheep and sheepfold 4 = 6 sheep. They add up to 25 sheep total and should meet all the specifications required.

Hope this helps :)