Love & Marriage

Algebra Level 1

A mathematician decided to stay married to his wife for as long as she (cumulatively) complimented him more often than she nagged him. Once the cumulative nagging caught up with the cumulative compliments, he would divorce her.

If N N is the number of years since the wedding, he determined that the cumulative number of compliments was 40 N 40N , while the cumulative amount of nagging was 2 N 2 2N^{2} . Assuming he stayed true to his word, for how many years did he stay married to his wife?


The answer is 20.

Denton Young by Denton Young , 47, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Denton Young
Jun 17, 2016

We need to find when 40 N − 2 N 2 40N - 2N^{2} reaches 0.

40 N 40N = 2 N 2 2N^{2}

Dividing by N

40 = 2 N 2N

N = 20

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

I sure hope this isn't reflective of your personal life!

It would be better to explicitly use inequalities, instead of an equation, to represent this problem. In this way, if we do not obtain an integer answer, we know which bound to look at.

The phrasing "after how many years did he divorce his wife" needs to be clarified. What is the starting point?

Calvin Lin Staff - 4 years, 12 months ago

Log in to reply

The day they were married.

Denton Young - 4 years, 12 months ago

It is not reflective of MY personal life.

However, the great mathematician Leibniz once was deciding whether to marry a certain woman. He made two lists -- one of advantages to being married to her, and the second of disadvantages. The second list was longer, so he didn't marry her.

Denton Young - 4 years, 12 months ago

Log in to reply

I sure hope it was a weighted list!

Can you edit the problem to indicate the starting date? Alternatively ask "for how many years was he married to his wife".

Calvin Lin Staff - 4 years, 12 months ago

Log in to reply

My source didn't specify.

Edited as suggested.

Denton Young - 4 years, 12 months ago
Hung Woei Neoh
Jun 19, 2016

We need to find the value of N N such that the amount of compliments is the same as the amount of nagging.

40 N = 2 N 2 N 2 = 20 N N 2 − 20 N = 0 N ( N − 20 ) = 0 N = 0 , N = 20 40N = 2N^2\\ N^2 = 20N\\ N^2 - 20N = 0\\ N(N-20) = 0\\ N=0,\;N=20

We take the positive value of N N , therefore N = 20 N=\boxed{20}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...