If x varies inversely as y and \(x = \frac{2}{3}\) when y = 9, find the value of y when \(x=\frac{3}{4}\)
A
\(\frac{1}{18}\)
B
\(\frac{8}{81}\)
C
\(\frac{9}{2}\)
D
8
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(x \propto \frac{1}{y}\)
\(x = \frac{k}{y}\)
\(\frac{2}{3} = \frac{k}{9}\)
\(3k = 18 \implies k = 6\)
\(x = \frac{6}{y}\)
When y = \(\frac{3}{4}\),
x = \(\frac{6}{\frac{3}{4}}\)
= \(\frac{6 \times 4}{3}\)
= 8
Source: WAEC / JAMB / NECO Classroom Archive (Record #26452)