Question

in a jar there are 70 marbles of three colours red,whiteand blue,if red:white is 2:3 and white:blue is 4:5 how many of them are red?

Answer 1

$$\begin{array}{l} \frac{r}{w} = \frac{2}{3} \Rightarrow r = \frac{2w}{3}; \frac{w}{b} = \frac{4}{5} \Rightarrow b = \frac{5w}{4}; r + b + w = 70 \\ \frac{2w}{3} + \frac{5w}{4} + w = 70; \frac{8w + 15w + 12w}{12} = 70 \\ w = \frac{70 \cdot 12}{35} = 24; r = \frac{2}{3} \cdot 24 = 16 \\ \end{array}$$

Answer: red=16