A carpenter agrees to work under the conditions that he is to be paid $5.50 every day he works, but must pay $6.60 every day he does not work. At the end of 30 days he finds he has paid out as much as he has received. How may days did he work?

5.5x = 6.6(30-x)

I don't get an integer solution. Is there a typo?

Let x = days worked

Let 30 - x = days not worked, so
$5.5 * x - $6.6 * (30 - x) = 0
days worked = 16 and 4/11 days
days not worked = 13 and 7/11 days.
Goofy answers, as far as I'm concerned!

To solve this problem, we need to find the number of days the carpenter worked. Let's assume the carpenter worked for 'x' number of days.

According to the given conditions:
- He is paid $5.50 every day he works.
- He pays $6.60 every day he does not work.

So, if the carpenter worked for 'x' days, he received a total of (5.50 * x) dollars.
If he didn't work for the remaining (30 - x) days, he paid a total of (6.60 * (30 - x)) dollars.

According to the problem statement, the carpenter finds that he has paid out as much as he has received. We can set up the following equation:

5.50 * x = 6.60 * (30 - x)

Now, let's solve this equation to find the value of 'x'.

5.50x = 198 - 6.60x (distributed 6.60 to be)

5.50x + 6.60x = 198 (combined like terms)

12.10x = 198 (added the x terms)

x = 198 / 12.10 (divided both sides by 12.10)

x ≈ 16.36 (rounded to the nearest whole number)

Since we cannot have a fraction of a day, the carpenter worked approximately 16 days.

Therefore, the carpenter worked for 16 days.