For a, you need to make the inequality 5+(-16t^2+128t+5)>150 and solve that. for b) just plug it in it's 14*11/2=77.
the guest answer is entirely wrong because the math expressions in the problem aren't as they should be, but i think i interpreted it right. nevertheless otherwise the guest did it right based on what the question said so dont be too hard on him/her.
Hope this helped!