S1 Expectation of discrete random variable question

Really stuck on this! Wondering if anyone could help me?

The random variable T has mean 20 and standard deviation 5. It is required to scale T by using the transformation S=aT+b, where a and b are constants (a>0), so that E(s) = 100 and Var (S) = 225

I created 2 simultaneous equations -

1) 100=20a+b
2) 225=25a+b
therefore 5a = 125, a=25
and b= 225-625 = -400

But the answer is a=3 and b=40

Why am I wrong? (thanks in advance)

Your second equation is incorrect.

Var(S) = a^2 Var(T)