To solve this question, let's start by writing down what we know. First of all, let's make a variable, x, which will stand for the number of women at the party (because that's what we want to find). Using this variable, we know:
2/3x have jewelry
1/4x have a black dress
Half the people wearing a black dress also have jewelry, so we know that there is an overlap of 1/4x ÷ 2 = 1/8x between the jewelry and black dress.
To account for this overlap, we can subtract it from both sides. We get
2/3x - 1/8x = 13/24x
1/4x - 1/8x = 1/8x
We know that there are 50 more women with a black dress, so:
13/24x = 1/8x + 50
Simplifying, we get:
13/24x = 3/24x + 50
10/24x = 50
x = 50*24/10 = 120
That means that there were 120 women at the party.
