What am I doing wrong in this algebra excercise?

This is my first question here, so please forgive me if the format etc. are not quite right. I've been attacking an algebra question, and my workings are below. There's a mistake somewhere (I don't know where) because my workings don't reach the correct answer! I'd really appreciate someone letting me know where I'm slipping up:

I have two functions, $G$ as a function of $N$ and $N$ as a function of $l:$

$G(N) = \frac{N}{40}\cdot 100$

$N(l) = \frac{300}{l} + 5$

I need to compose a function that represents $G$ as a function of $l.$ I do it like this:

$$G(l) = \frac{\frac{300}{l}+5}{40}\cdot 100 = \frac{\frac{100 \cdot 300}{l} + 100 \cdot 5}{40}=\frac{\frac{30,000}{l} + 500}{40}= \frac{750}{l} + 12.5$$

And that's it. ...but it's wrong.

Thanks so much for your help with this!

• See meta.math.stackexchange.com/questions/5020/… for formatting. – lhf Jul 10 '14 at 12:19
• Why do you say that the answer is wrong? What result did you expect? – mfl Jul 10 '14 at 12:23
• The arithmetic adds up... Is there an answer key somewhere? – abiessu Jul 10 '14 at 12:28
• Correct as far as eye can see. – user21820 Jul 10 '14 at 12:30

$$G(N) = \frac{5}{2} N = \frac{5}{2} \cdot 300 \cdot \frac{1}{l} + \frac{5}{2} \cdot 5 = 750 \frac{1}{l} + 12.5$$