Question

If A:B=2:3 and B:C=4:5 and 5A:3C is --------- ?

Answer 1

A:B is 2:3 which means A/B=2/3. Also, B:C=4:5 which means B/C=4/5. You need a combination with A and C in your answer. You just have to solve for A and C in each equation and not worry about the fact there's a B still present. In these types of questions, it will usually disappear, as I'm about to show you:

If A/B=2/3, then A = 2B/3. Also, C = 5B/4. Therefore, 5A = 10B/3 and 3C = 15B/4. Dividing, you have: \[\frac{5A}{3C}={\frac{\frac{10B}{3}}{\frac{15B}{4}}}=\frac{10B}{3} \times \frac{4}{15B}=\frac{2}{3}\]Note how the Bs cancelled.

Good luck with the rest - I need sleep :)

Answer 2

Oh - to be technically finished, you should write:

5A:3C = 2:3