A chess club currently has 37 male members and 16 female members. The club hosted a Valentine's Day event to attract married couples to join the club as new members. (Both husband and wife must be totally new to the club.) After this event, the percentage of female members became 40%. Find the number of married couples who joined the club after the event.

1. Define the unknown and express the new numbers of male, female and total members.

Let the number of married couples who joined be $x$.

Since each couple has one husband and one wife,

New number of female members $=16+x$.

New total number of members $=37+16+2x=53+2x$.

2. Form an equation using the given female percentage.

After the event, female members made up $40\%$ of the club.

$\frac{16+x}{53+2x}=40\%=\frac{40}{100}=\frac{2}{5}$

3. Solve the linear equation for the number of couples.

$5(16+x)=2(53+2x)$

$80+5x=106+4x$

$x=26$

This gives $x=26$, but this is not consistent with the percentage increasing from $\frac{16}{53}\approx30.2\%$ to $40\%$? Check the algebra:

$80+5x=106+4x \Rightarrow x=26$

So $26$ married couples joined.