the number of men in the U.S. Senate totaled 4 more than 5 times the number of women. Find the number of men and women, given the senate has 100.

Question

Here's the complete question;

For a recent year, the number of men in the U.S. Senate totaled 4 more than 5 times the number of women. Find the number of men and women in the Senate given that the Senate has 100 members total.I do not know how to set up the equation.

I don't know how to set up the equation.

Answer 1

The problem gives you the number of men in terms of the number of women so let's start with the number of women.

 

Let W = number of women

 

Because there are 100 senators total, if there are W women, that leaves the number of men as (100 - W)

 

Now that we have an expression for the number of men and the number of women, we can write our equation.

 

4 more than 5 times means you multiply by 5 and then add 4.

 

The number of men (100 - W) is (equals) 5W (number of women) + 4

 

So taking away all the words we get

 

100 - W = 5W + 4

 

Now you add W to both sides

 

100 = 6w + 4

 

Now you subtract 4 from both sides

 

96 = 6w

 

Now divide both sides by 6

 

16 = W

 

Therefore 100 - W = 100 - 16 = 84

 

So there are 16 women and 84 men.

 

let me know if you have any questions