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

Commented by Tawa1 last updated on 08/Apr/19

a : b = 4 : 9 ∴ (a/b) = (4/9) ∴ 9a = 4b ∴ a = ((4b)/9) >>>>> note Second one b : c = 3 : 7 ∴ (b/c) = (3/7) ∴ 3c = 7b ∴ c = ((7b)/3) >>>>> note Now, a : b : c = ((4b)/9) : b : ((7b)/3) multiply through by L.C.M which is 9 Now, a : b : c = (((4b)/9) × 9) : (b × 9) : (((7b)/3) × 9) Now, a : b : c = 4b : 9b : (7b × 3) Now, a : b : c = 4b : 9b : 21b b will cancel out. Now, a : b : c = 4 : 9 : 21

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

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

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

$${a}:{b}=\mathrm{4}:\mathrm{9} \\ $$$$\:\:\:\:{b}:{c}=\mathrm{9}:\mathrm{21} \\ $$$${a}:{b}:{c}=\mathrm{4}:\mathrm{9}:\mathrm{21} \\ $$

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

((a,:,b,:,c),(4,,9,,),(,,3,,7),(−,−,−,−,−),(4,:,9,:,(21)) )

$$\begin{pmatrix}{{a}}&{:}&{{b}}&{:}&{{c}}\\{\mathrm{4}}&{}&{\mathrm{9}}&{}&{}\\{}&{}&{\mathrm{3}}&{}&{\mathrm{7}}\\{−}&{−}&{−}&{−}&{−}\\{\mathrm{4}}&{:}&{\mathrm{9}}&{:}&{\mathrm{21}}\end{pmatrix} \\ $$

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