The sheeps

Algebra Level 3

One fourth of heard of goats was seen in the forest. Twice the square root of the number of the heard had gone up the hill and the remaining 15 goats were on the bank of river. Find the total number of goats.

The answer is 36.

3 solutions

Cat H
Nov 30, 2016

Since the answer $x$ must be an integer, it must be a perfect square that is greater than 15 and divisible by 4. These conditions limit the possible answers to only a few - 16, 36, 64, 100, etc, which can then be tested using the equation:

$\frac{x}{4}$ +15+2*( $x$ ^ $\frac{1}{2}$ ) = $x$

Hence, the answer is found to be 36.

Am I the only one who found the phrasing of this question to be very confusing? I thought the forest was the whole area containing the hill and the river bank and that the total number of goats described needed to be multiplied by four to get the whole answer. It would have made sense imo if the first sentence said that one fourth of the heard was just "in the forest" without the word "seen" or something to imply that there were three separate locations.

Tristan Goodman - 2 years, 3 months ago

Mohd Naim Mohd Amin
Apr 30, 2014

Hello , as for this type of problem,

let x = total number of goats,

x/4 + 2(x)^(0.5) + 15 = x

x + 8(x)^(0.5) + 60 = 4x

3x - 60 = 8(x)^(0.5)

By squaring both sides,

(3x - 60)(3x - 60) = 64x

9x^(2) - 424x - 3600 = 0

( x- 36 ) ( 9x -100) = 0

x =36 ,or x = 100/9,

we'll take 36(whole number) instead of decimals (100/9) because the number of goats is not decimals,

therefore x = 36....

Yagna Teja
Apr 19, 2014

let X be the total goats then according to question X/4+2square root(X)+15=X then X=6

Yagna Teja . I believe you meant 36.

Guiseppi Butel - 7 years, 1 month ago

The sheeps

The answer is 36.

3 solutions

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