Shorter proof for this?

Question

if $G = T + N$ and $T = N * t$, where $t$ is a $\%$, find $T$ if the only given values are $G$ and $t$.

I already has a formula but it needs to compute for $N$ first which is lengthy, is there a shorter formula without computing for $N$ first?

Please help. Thanks in Advance.

Answer 1

$$G=N\cdot t+N=N\cdot(1+t)$$ $$N=\frac{G}{1+t}$$ $$T=\frac{G\cdot t}{1+t}$$