# Question #2dc91

Feb 1, 2018

The third person will have to pay 1/6 of the cost.

#### Explanation:

Let the total cost be $x$
One of the three agrees to pay $\frac{1}{2} x$, and other agrees to pay $\frac{1}{3} x$
So, the amount remaining to be payed will be:

$x - \frac{1}{2} x - \frac{1}{3} x$

Equating the denominators:

$= x \left(\frac{6}{6}\right) - \frac{1}{2} \left(\frac{3}{3}\right) x - \frac{1}{3} \left(\frac{2}{2}\right) x$

$= \frac{6 x - 3 x - 2 x}{6}$

$= \frac{x}{6}$

So, the third person will have to pay 1/6 of the cost.

Feb 1, 2018

$\frac{1}{6}$

#### Explanation:

$\text{the total cost can be represented by } 1$

$\text{adding the fractions } \frac{1}{2} + \frac{1}{3}$

$\text{the "color(blue)"lowest common multiple "" of 2 and 3 is 6}$

$\Rightarrow \frac{1}{2} + \frac{1}{3} = \left(\frac{1}{2} \times \frac{3}{3}\right) + \left(\frac{1}{3} \times \frac{2}{2}\right) = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$

$\text{third person has to pay } 1 - \frac{5}{6} = \frac{6}{6} - \frac{5}{6} = \frac{1}{6}$

$\text{third person pays "1/6" of the cost}$