# Question #5d437

May 27, 2017

$b \to \frac{1}{3}$

#### Explanation:

There are three groups of people. Let them be ${g}_{1} \text{; "g_2"; } {g}_{3}$
Let the total count be ${g}_{t}$

.........................................................................................................
One half of the employees earn:

${g}_{1} = \frac{1}{2} \times {g}_{t} > 18000$

The remainder at this point is $\frac{1}{2} {g}_{t}$
.............................................................................................................
One third of the remainder earn:

${g}_{2} \to 15000 < \left[\frac{1}{3} \left(\frac{1}{2} {g}_{t}\right)\right] < 18000$
............................................................................................................

What part of the staff earn less than 15000

This is a question just about fractions

The remainder is $\text{ } {g}_{3} = \left[1 - \frac{1}{2} - \left(\frac{1}{3} \times \frac{1}{2}\right)\right] {g}_{t}$

$\frac{1}{2} - \left(\frac{1}{3} \times \frac{1}{2}\right)$

$\frac{1}{2} - \frac{1}{6}$

$\frac{3}{6} - \frac{1}{6} \text{ "=" "2/6" "=" } \frac{1}{3}$