Question

If a, b, c are positive integers such that
a/3=b/4=c/5
and abc = 1620,
find the value of b

​

Answer 1

Step-by-step explanation:

$Given: \: \frac{a}{3} = \frac{b}{4} = \frac{c}{5} \\ \: Let \: \:\:\frac{a}{3} = \frac{b}{4} = \frac{c}{5} = k \\ \implies \: \frac{a}{3} =k \implies \: a = 3k \\ \implies \: \frac{b}{4} =k \implies \: b = 4k \\ \implies \: \frac{c}{5} =k \implies \: c = 5k \\ \because \: abc = 1620 \\ \implies (3k)(4k)(5k) = 1620 \\ \implies 60k^{3} = 1620 \\ \implies k^{3} = \frac{1620}{60} \\ \implies k^{3} = 27 \\ \implies k= 3 \\ \because \: b = 4k \\ \therefore \: b = 4 \times 3 \\ \implies \: \huge \fbox{b = 12}$