In a group of 32 men and women, there are 6 more women than men. How many people of each gender are there?

Method 1 :

Let n be the number of women.
Then, number of men = n - 6

n + (n - 6) = 32
2n - 6 = 32
2n = 38
n = 19
n - 6 = 13

There are 19 women and 13 men.


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Method 2 :
Let w be the number of women, and m be the number of men.

w + m = 32 …… [1]
w - m = 6 …… [2]

[1] + [2] :
(w + m) + (w - m) = 38
2w = 38
w = 19

[1] - [2] :
(w + m) - (w - m) = 26
2m = 26
m = 13

There are 19 women and 13 men.

w = m + 6
w + m = 32
Solve the system of equations.
m + 6 + m = 32
2m = 26
m = 13
w = 19

19 women and 13 men

13 men and 19 women

19 women
and
13 men.

32/2=16

16+6= 22

There's 16 men and 22 women.

Let there be x men and x+6 women
x+(x+6) = 32
2x+6 = 32
2x=32-6
2x=26
x= 13 (number of men)
13+6 = 19 (number of women)

32-6=26. 26/2=13. 13 men and 19 women.

w + m = 32
w = m + 6

2m + 6 = 32
m = 13
w = 19

13 men and 19 women

Women: (32 + 6)/2 = 19
Men: (32 - 6)/2 = 13

Divide by two to make two equal halves.
Add 3 women.
Subtract 3 men (total 6 difference)

32/2 = 16

16 + 3 = 19 women
16 - 3 = 13 men