Question

2/3 of the women at the party wear jewelry. 1/4 of the women wear a black dress. If there are 50 more women wearing jewelry than women with a black dress and half the women wearing a black dress also wear jewelry then how many women are there at the party?
please explain how to set up the equation to solve

i need to know for an important exam

Answer 1

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.