JAMB - Mathematics (1985 - No. 1)
If three numbers P, Q, R are in ratio 6 : 4 : 5, find the value of \(\frac{3p - q}{4q + r}\)
\(\frac{3}{2}\)
\(\frac{2}{3}\)
2
3
18
Explanation
P : Q : r = 6 : 4 : 5
5 = 6 + 4 + 5
= 15
P = \(\frac{6}{15}\), q = \(\frac{4}{15}\), r = \(\frac{5}{15}\) = \(\frac{1}{3}\)
To find \(\frac{3p - q}{4q + r}\)
3p - q = 3 x \(\frac{6}{15}\) - \(\frac{4}{15}\)
\(\frac{18}{15}\) - \(\frac{4}{15}\) = \(\frac{14}{15}\)
∴ 4q + r = 4 x \(\frac{4}{15}\) + \(\frac{5}{15}\)
\(\frac{16}{15}\) = \(\frac{16}{15}\) + \(\frac{5}{15}\)
= \(\frac{21}{15}\)
\(\frac{14}{15}\) x \(\frac{15}{21}\) = \(\frac{14}{21}\)
= \(\frac{2}{3}\)
5 = 6 + 4 + 5
= 15
P = \(\frac{6}{15}\), q = \(\frac{4}{15}\), r = \(\frac{5}{15}\) = \(\frac{1}{3}\)
To find \(\frac{3p - q}{4q + r}\)
3p - q = 3 x \(\frac{6}{15}\) - \(\frac{4}{15}\)
\(\frac{18}{15}\) - \(\frac{4}{15}\) = \(\frac{14}{15}\)
∴ 4q + r = 4 x \(\frac{4}{15}\) + \(\frac{5}{15}\)
\(\frac{16}{15}\) = \(\frac{16}{15}\) + \(\frac{5}{15}\)
= \(\frac{21}{15}\)
\(\frac{14}{15}\) x \(\frac{15}{21}\) = \(\frac{14}{21}\)
= \(\frac{2}{3}\)
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