Discussion
The sum of two numbers is 84 and their HCF is 6. If the ratio of the numbers is 3 : 11, find the larger number.
Answer: A
The larger number is 66.
With the ratio 3 : 11, write the numbers as \(3k\) and \(11k\):
\[ \begin{aligned} 3k + 11k &= 84 \\ 14k &= 84,\ k = 6 \\ \text{numbers} &= 18 \text{ and } 66 \end{aligned} \]
Check the HCF: since 3 and 11 have no common factor, the HCF of 18 and 66 is \(k = 6\), as given. 60, 54 and 48 do not combine with any partner in the ratio 3 : 11 to make 84.
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