If \(6A=14B\) then the ratio of \(\displaystyle\frac{A}{7}\) to \(\displaystyle\frac{B}{6}\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2:1
The equation \(6A=14B\) fixes the ratio of A to B, so both can be written as multiples of one number \(k\); that number then cancels in the required ratio.
From \(6A=14B\): \(\displaystyle\frac{A}{B}=\frac{14}{6}=\frac{7}{3}\), so \(A=7k\) and \(B=3k\)
The first quantity: \(\displaystyle\frac{A}{7}=\frac{7k}{7}=k\)
The second quantity: \(\displaystyle\frac{B}{6}=\frac{3k}{6}=\frac{k}{2}\)
Their ratio, with \(k\) cancelling: \(k:\frac{k}{2}=2:1\)