Question #96753

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Answer 1 · 2017-10-30T11:15:14

#36#

Let #x# represent the number of camels.

We then have:

#x-(x/4+2sqrt(x))=15#

i.e. total number of camels - the number seen in forest and in the mountains, leaving 15 remaining.

Removing bracket and collecting terms:

#3/4x-2sqrt(x)=15#

Multiplying by 4:

#3x-8sqrt(x)=60= 3x-8sqrt(x)-60=0#

Let #x = t^2#

#3t^2-8sqrt(t^2)-60=3t^2-8t-60=0#

#3t^2-8t-60=0#

Factoring:

#(3t+10)(t-6)=0=> t= 6 or t=-10/3#

Only #t=6# is valid here:

So #t=6# , but #t^2=x#

#:. x=36#