how to proceed ? Have I correctly transformed the question to an equation?

Amongst Teaching staff of ABC university the ratio of men and women is $5:2$. Amongst the women $\large\frac{3}{7}$ are not married . If the number of married women teacher is $56$ then the total number of teacher is ?

What I have tried :

$$M:W=5:2$$

$$W_{\text{unmarried}}= \frac{3}{7}W$$

$$W_{\text{married}}= 56$$

now what to do?

$$W=W_{\text{unmarried}}+W_{\text{married}}$$

$$W = \frac{3}{7}W + 56$$ $$W= 98$$

• You can only accept one answer so choose wisely. Later you'll earn privilege to vote on questions and answers. – user171358 Oct 30 '14 at 16:30

Yes You're right

Let $x$ and $y$ be number of Male and Female teachers $$2x=5y\tag{1}$$

$\large\frac{3}{7}$ Females are unmarried that means , $\large\frac{4}{7}$ Females are married and number of married Females is also $56$

$$56=\frac{4y}{7}\tag{2}$$ After Solving $(1)$ and $(2)$ simultaneously we get $$x=245 \quad, \quad y=98$$

and $$\text{Total Number of Teachers} =343$$

$\dfrac{M}{W}=\dfrac{5}{2}=t \implies W=2t$

$\dfrac{4}{7}W=56 \implies W=98$

$\therefore t=49 \implies M=490$

Hint: If $T$ is the total number of women, you know that $\frac{3}{7}T$ are not married and therefore $\frac{4}{7}T$ are married. So, $\frac{4}{7} T = 56$, so $T =\,...$ Can you finish?

The trick is to maintain units, and not just work with numbers.

5 men : 2 wom : 7 prof

3 wu : 4 wm : 7 wom

56 wm * 7 wom / 4 wm * 7 prof / 2 wom = 56 /8 *7 *7 * wm/wm * wom/wom * prof

= 343 prof