Question 226362
Write an equation for each statement
:

Wark’s (W) age equals Peter’s (P) age plus the cube root of Ian’s (I) age.
W = P + {{{I^(1/3)}}}
:
P’s age equals I’s age plus the cube root of W’s age, plus 14 years.
P = I + {{{W^(1/3)}}} +14
;
I’s age equals the cube root of W’s age plus the square root of P’s age.
I = {{{W^(1/3)}}} + {{{sqrt(P)}}}


What is the age of each ??? 
:
This looks horrible at first glance but there are only 3 perfect cubes
in the age range. Ignoring 1, we have 8, 27 & 64, for I and W. And P is
a perfect square.
:
In first equation
W = P + {{{I^(1/3)}}}
W = 27, I=8, then P=25
or
W = 8, I=64, P=4; (does not work in the other equations)
:
Test in the 2nd equation using W=27; I=8; P=25
P = I + {{{W^(1/3)}}} +14 
25 = 8 + {{{27^(1/3)}}} + 14; this works,
;
Test in the 3rd equation
I = {{{W^(1/3)}}} + {{{sqrt(P)}}}
8 = {{{27^(1/3)}}} + {{{sqrt(25)}}}
8 = 3 + 5
:
The ages; Warks: 27; Peters 25; Ian 8