A father agrees to give his son 2000 tugriks for each day the son cleans the house and deduct 3000 tugriks for each day he doesn't clean. After 60 days, the son has not received any money. How many days did the son clean?

1. Problem Description

A father agrees to give his son 2000 tugriks for each day the son cleans the house and deduct 3000 tugriks for each day he doesn't clean. After 60 days, the son has not received any money. How many days did the son clean?

2. Solution Steps

Let $x$ be the number of days the son cleaned the house.

Let $y$ be the number of days the son did not clean the house.

The total number of days is 60, so we have:

$x + y = 60$

The total amount of money the son earned is

0. The son earns 2000 tugriks for each day he cleans and loses 3000 tugriks for each day he doesn't. So:

$2000x - 3000y = 0$

We have a system of two equations with two variables:

$x + y = 60$

$2000x - 3000y = 0$

From the first equation, we can express $y$ in terms of $x$:

$y = 60 - x$

Substitute this into the second equation:

$2000x - 3000(60 - x) = 0$

$2000x - 180000 + 3000x = 0$

$5000x = 180000$

$x = \frac{180000}{5000}$

$x = 36$

Now we can find $y$:

$y = 60 - x = 60 - 36 = 24$

So the son cleaned for 36 days and didn't clean for 24 days.

We can check if this is correct:

$2000(36) - 3000(24) = 72000 - 72000 = 0$

3. Final Answer

The son cleaned for 36 days.