Question

If A : B = 5 : 6 and B : C = 9 : 11 , then find A : B : C

Answer 1

Answer:

$\: \: \: \: a \: \: \: ratio \: \: \: b \: \: \: \: ratio \: \: \: c = 45 \: \: \: \: ratio \: \: \: \: 54 \: \: ratio \: \: \: \: \: 66.$

Step-by-step explanation:

$\frac{a}{b} = \frac{5}{6} \\ \\ \frac{b}{c} = \frac{9}{11} \\ \\ multiply \: both \: equations \: \: \: we \: get \\ \\ \frac{a}{c} = \frac{5}{6} \times \frac{9}{11} \\ \\ \frac{a}{c} = \frac{5}{11} \times \frac{3}{2} = \frac{15}{22} \\ \\ therefore \: \: \: \frac{c}{a} = \frac{22}{15} \\ \\ then \: \: \: a = \frac{5}{6} b = \frac{5*9}{6*11} c \\ \\ therefore \: \: \: \frac{a}{5} = \frac{b}{6} = \frac{9c}{66} \\ \\ then \: \: \frac{a}{45} = \frac{b}{54} = \frac{c}{66} \\ \\ so \: \: \: \: a \: \: \: ratio \: \: \: b \: \: \: \: ratio \: \: \: c = 45 \: \: \: \: ratio \: \: \: \: 54 \: \: ratio \: \: \: \: \: 66.$