Aherd of horses split and went to three areas. one fourth of the herd of horses was seen in the forest. twice the square root of the herd had gone to the mountain slopes, and three times five horses remained on the riverbank. what is the numerical measure of that herd of horses

the total number of horses in the herd is 36

Step-by-step explanation:

Let x represent the total number of horses in the herd.

One fourth of the herd of horses was seen in the forest. This means that the number of horses that was seen in the forest would be

1/4 × x = x/4

Twice the square root of the herd had gone to the mountain slopes. This means that the number of horses that had gone to the mountain slopes would be

2 × √x = 2√x

Three times five horses remained on the riverbank. This means that the number that remained would be

3 × 5 = 15

Therefore

x/4 + 2√x + 15 = x

x - x/4 - 15 = 2√x

(4x - x - 60)/4 = 2√x

(3x - 60)/4 = 2√x

Cross multiplying,

3x - 60 = 8√x

Squaring both sides of the equation, it becomes

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

9x² - 180x - 180x + 3600 = 64x

9x² - 360x - 64x + 3600 = 0

9x² - 424x + 3600 = 0

Applying the quadratic equation

x = (- b ±√b² - 4ac)/2a

x = ( - - 424 ± √-424² - 4(9 × 3600)/2 × 9

x = (424 ± √179776 - 129600)/18

x = (424 ±√50176)/18

x = (424 + 224)/18 or

x = (424 - 224)/18

x = 36 or x = 11.11

the number of horses must be whole number. Therefore, the number of horses is 36

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.