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Question Number 57601 by ketto2 last updated on 08/Apr/19

Commented by Tawa1 last updated on 08/Apr/19

$$\mathrm{a}:\mathrm{b}=4:9$$$$\therefore \frac{\mathrm{a}}{\mathrm{b}}=\frac{4}{9}$$$$\therefore 9\mathrm{a}=4\mathrm{b}$$$$\therefore \mathrm{a}=\frac{4\mathrm{b}}{9}>>>>>\mathrm{note}$$$$\mathrm{Second}\mathrm{one}$$$$\mathrm{b}:\mathrm{c}=3:7$$$$\therefore \frac{\mathrm{b}}{\mathrm{c}}=\frac{3}{7}$$$$\therefore 3\mathrm{c}=7\mathrm{b}$$$$\therefore \mathrm{c}=\frac{7\mathrm{b}}{3}>>>>>\mathrm{note}$$$$\mathrm{Now},\mathrm{a}:\mathrm{b}:\mathrm{c}=\frac{4\mathrm{b}}{9}:\mathrm{b}:\frac{7\mathrm{b}}{3}$$$$\mathrm{multiply}\mathrm{through}\mathrm{by}\mathrm{L}.\mathrm{C}.\mathrm{M}\mathrm{which}\mathrm{is}9$$$$\mathrm{Now},\mathrm{a}:\mathrm{b}:\mathrm{c}=\left(\frac{4\mathrm{b}}{9}\times 9\right):\left(\mathrm{b}\times 9\right):\left(\frac{7\mathrm{b}}{3}\times 9\right)$$$$\mathrm{Now},\mathrm{a}:\mathrm{b}:\mathrm{c}=4\mathrm{b}:9\mathrm{b}:\left(7\mathrm{b}\times 3\right)$$$$\mathrm{Now},\mathrm{a}:\mathrm{b}:\mathrm{c}=4\mathrm{b}:9\mathrm{b}:21\mathrm{b}$$$$\mathrm{b}\mathrm{will}\mathrm{cancel}\mathrm{out}.$$$$\mathrm{Now},\mathrm{a}:\mathrm{b}:\mathrm{c}=4:9:21$$

Answered by $@ty@m last updated on 08/Apr/19

$$a:b=4:9$$$$b:c=9:21$$$$a:b:c=4:9:21$$

Answered by Rasheed.Sindhi last updated on 09/Apr/19

$$\left(\begin{array}{ccccc}a& :& b& :& c\\ 4& & 9& & \\ & & 3& & 7\\ -& -& -& -& -\\ 4& :& 9& :& 21\end{array}\right)$$

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