given A:B=3:7 and B:C=4:9 find A:C

Question

29-10-2022
Mathematics

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given A:B=3:7 and B:C=4:9 find A:C

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BannonZ290335 BannonZ290335 · Answer 1 · 2022-10-29T07:09:32+02:00

[tex]\begin{gathered} \frac{A}{C}=\frac{A}{B}\times\frac{B}{C} \\ \text{Thus,} \\ A\colon C=A\colon B\times B\colon C \end{gathered}[/tex][tex]\begin{gathered} A\colon B=\frac{A}{B}=\frac{3}{7} \\ B\colon C=\frac{B}{C}=\frac{4}{9} \\ \text{Thus,} \\ A\colon C=\frac{A}{C}=\frac{A}{B}\times\frac{B}{C} \\ A\colon C=\frac{3}{7}\times\frac{4}{9} \\ A\colon C=\frac{12}{63}=\frac{4}{21}=4\colon21 \end{gathered}[/tex]

Hence, A:C is 4:21