Question

one-fourth of a herd of elephants was seen in the forest. twice the square root of the herd had gone to mountain and the remaining 15 elephants were seen on the bank of the river.find the total number of elephants

Answer 1

let c = the total number of elephants.

We're given that c/4 elephants were in the forest, 2√c elephants were in the mountains, and 15 elephants were at the river. So,

c = c/4 + 2√c + 15

=> isolating √c
√c = 3c/8 - 15/2

=> squaring both sides
c = 9c^2/64 - 45c/8 + 225/4

=> multiplying both sides by 64
64c = 9c^2 - 360c + 3,600

=> moving terms to the LHS
9c^2 - 424c + 3,600 = 0

=> factoring
(9c - 100)(c - 36) = 0

Solutions for c include c = 100/9 and c = 36.

The only integer solution is c = 36. So, there are 36 elephants in the herd.

Hope you got your answer.