Question

If m/n = 6/5,then 3m+2n = ?

Answer 1

m/n=6/5
let the common multiple be x
m=6x
n=5x
3(6x)+2(5x)= 18x + 10x= 28x

Answer 2

Given the ratio $\frac mn=\frac 65$, so reversing the ratio, we get  $\frac nm=\frac 56$

we can calculate the value of  3m+2n in either terms of m or n

(i) In terms of m

When we take m common, we get

$m(3+\frac{2n}{m})$  

Substitute $\frac nm=\frac 56$, we get

$m(3+2* \frac 56) = m(3+\frac 53) = m(\frac{14}{3})=\frac{14m}{3}$  

(ii) In terms of n

When we take n common, we get

$n(\frac{3m}{n}+2 )$

Substitute $\frac mn=\frac 65$, we get

$n(3* \frac 65+2)=n(\frac{18}{5}+2)=n(\frac{28}{5})=\frac{28n}{5}$  

Hence the value of $3m+2n=\frac{28n}{5}=\frac{14m}{3}$