## Wednesday, May 18, 2016

### stretch your brain a bit

The number of male employees decreased by 10% compared to the previous year. The number of female employees increased by 15%. There are currently a total of 182 employees at the company. If there were 20 more male employees than female employees last year, how many female employees are at the company this year?

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Joe Walther said...

92.
Why? Because math.

Kevin Kim said...

My own procedure for tackling this problem:

1. Define "this year" and "last year" as 2016 and 2015, respectively.
2. Let #male & female employees in 2015 = m & f, respectively.
3. For 2015, let m = f + 20, i.e., m - f = 20.
4. #male employees in 2016 = 0.9m. (10% fewer than prev. yr.)
5. #female employees in 2016 = 1.15f. (15% more than prev. yr.)
6. Let 0.9m + 1.15f = 182. (current total, 2016)
7. Systems of equations:

0.9m + 1.15f = 182
m - f = 20

8. Multiply bottom equation by 1.15. System now looks like:

0.9m + 1.15f = 182
1.15m - 1.15f = 20

2.05m = 205

Therefore m = 100 and f = 80 (in 2015, remember)

80 * 1.15 = 92 female employees in 2016.

QED.

Kevin Kim said...

You look really, really serious in that photo, Joe. Sort of an "angry Jeremy Renner-as-sniper" thing going on.

Joe Walther said...

Thanks.
I think.