Just use algebra
Total = Subtotal + .15 Total
So
.85 Total = Subtotal
Total = Subtotal/.85
Var 3 = .15 Subtotal/.85 = 3 Subtotal/17
Or more thoroughly....
Let $B = $ base cost.
Var 1 = $.5*B$
Var 2 = $.1*B$
Fixed Cost = $4$
SubTotal = Var 1 + Var 2 + Fixed Cost = $.5B + .1B + 4.00 = .6B + 4.00$.
Var 3 = $.15*$ Total=$.15 X$.
$X$ = Total = Subtotal + Var 3 = $.6B + 4.00 + .15X$
So $X = .6B + 4 + .15X$
$X - .15X = .6B +4 + .15X - .15X$
$.85 X = .6B + 4$
$.85 X/.85 = (.6B + 4)/.85$
$X = \frac {.6}{.85}B + \frac 4{.85} = \frac {60}{85}B + \frac {400}{85}=\frac {12}{17}B + 4\frac {12}{17}$.
Var 3 = $.15X = .15(\frac {60}{85}B + \frac {400}{85}) = \frac 9{85}B + \frac {12}{17}=\frac 3{17}(.6B + 4) = \frac 3{17}Subtotal$