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Compound Variation

If a : b = ...

Question

If $a : b = 3 : 4$ and $b : c = 8 : 9,$ find $a : b : c .$

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Solution

$a : b = 3 : 4$
$b : c = 8 : 9$
$3 \times 8 : 4 \times 8 : 4 \times 9$
$24 : 32 : 36$
$6 : 8 : 9$ .

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