Discussion
The ratio of two numbers is 7 : 9 and their difference is 36. Find the smaller number.
Answer: B
The smaller number is 126.
Write the numbers as \(7k\) and \(9k\). Their difference is \(2k\):
\[ \begin{aligned} 9k - 7k &= 36 \\ k &= 18 \\ 7k &= 126,\ 9k = 162 \end{aligned} \]
Check: \(162 - 126 = 36\) and \(126 : 162 = 7 : 9\). 112 is \(7 \times 16\), which would need a difference of 32, 168 is \(7 \times 24\), which would need 48, and 144 is not a multiple of 7 at all.
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