Last year, a choir club had 32 members in total. This year, the number of male members increased by 25% and the number of female members increased by 15%. The number of increased members was the same for both males and females. Let $x$ be the number of male members last year and $y$ be the number of female members last year. Find the number of male and female members this year.

1. Problem Description

Last year, a choir club had 32 members in total. This year, the number of male members increased by 25% and the number of female members increased by 15%. The number of increased members was the same for both males and females. Let $x$ be the number of male members last year and $y$ be the number of female members last year. Find the number of male and female members this year.

2. Solution Steps

First, we can set up two equations based on the given information:

The total number of members last year was 32:

$x + y = 32$

The number of male members increased by 25% and the number of female members increased by 15%. The increase in the number of male members is $0.25x$ and the increase in the number of female members is $0.15y$. These two increases are equal:

$0.25x = 0.15y$

We can rewrite the second equation as:

$25x = 15y$

$5x = 3y$

$x = \frac{3}{5}y$

Substitute $x = \frac{3}{5}y$ into the first equation:

$\frac{3}{5}y + y = 32$

$\frac{8}{5}y = 32$

$y = 32 \times \frac{5}{8}$

$y = 4 \times 5$

$y = 20$

Now, we can find $x$:

$x = \frac{3}{5} \times 20$

$x = 3 \times 4$

$x = 12$

So, last year there were 12 male members and 20 female members.

Now, we need to find the number of male and female members this year.

The number of male members this year is $x + 0.25x = 1.25x = 1.25 \times 12 = 15$.

The number of female members this year is $y + 0.15y = 1.15y = 1.15 \times 20 = 23$.

3. Final Answer

The number of male members this year is 15 and the number of female members this year is

2

3.