SOLUTION: A group of 165 men and women visit a cinema. There are 20% more men than women. How many men are there in the group? The answer is 90 but I don't understand how you work it ou

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A group of 165 men and women visit a cinema. There are 20% more men than women. How many men are there in the group? The answer is 90 but I don't understand how you work it ou      Log On


   

Question 1020248: A group of 165 men and women visit a cinema.
There are 20% more men than women.
How many men are there in the group?
The answer is 90 but I don't understand how you work it out, and if there is a formula for these types of questions?
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Name your variables.
M%2BW=165 "group of 165 men and women"
.
.
M=W%281%2B20%2F100%29"20% more men than women"
M=%28120%2F100%29W
M=%286%2F5%29W
Substitute into your first equation and solve for W.
%286%2F5%29W%2BW=165
%286%2F5%29W%2B%285%2F5%29W=165
%2811%2F5%29W=165
W=%285%2F11%29165
Solve for W.
Then use either equation to solve for M.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
m = number of men
w = number of women.

m + w = 165

you are told that there are 20% more men than women.

this means that m = w + 20% of women, which means that m = w + .2 * w, which means that m = 1.2 * w.

m + w = 165 becomes 1.2 * w + w = 165, after you replace m with its equivalent value of 1.2 * w.

1.2 * w + w = 165 become 2.2 * w = 165.

divide both sides of this equation by 2.2 to get w = 165 / 2.2

solve for w to get w = 75.

since m = 1.2 * w, then m = 1.2 * 75 = 90

there are 90 men and 75 women.

your solution is there are 90 men in the group.