Question 1207641: Hi
The number of men is more than the number of women. 20% of men and 25% of women are unmarried. The number of unmarried men and unmarried women are equal. A total of 230 employees are unmarried. What is the percentage of women . My son tried to solve it but the number of employees was in fractions.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this is what i get.
let x = number of men
let y = number of women
you are given that 20% of men and 25% of women are unmarried.
the equation for that is .2x + .25y = number of unmarried employees.
a total of 230 employees are unmarried.
the equation for that is .2x + .25y = 230
the number of unmarried men and unmarried women are equal.
that gets you .2x = .25y
if .2x + .25y = 230, and .2x = .25y, then replace .2x with .25y to get:
.25y + .25y = 230
combine like terms to get .5y = 230
solve for y to get y = 230 / .5 = 460.
likewise replace .25y with .2x to get:
.2x + .2x = 230
combine like terms to get:
.4x = 230
solve for x to get x = 230 / .4 = 575.
you have 575 men and 460 women for a total of 1035 employees.
the percentage of women is 460 / 1035 * 100 = 44.4444444.....%.
the percent is a fraction, but the number of employees is not.
working from the beginning, you have:
575 men and 460 women.
20% of the men and 25% of the women are unmarried.
that makes .20 * 575 + .25 * 460 unmarried employees = 115 men and 115 women that are unmarried.
that makes a total of 230 employees that are unmarried, with the number of unmarried men being equal to the number of unmarried women.
let me know if this helps.
theo
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
The number of men is more than the number of women. 20% of men and 25% of women are unmarried.
The number of unmarried men and unmarried women are equal. A total of 230 employees are unmarried.
What is the percentage of women . My son tried to solve it but the number of employees was in fractions.
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Another solution.
We are given that a total of 230 employees are unmarried.
We are also given that the number of unmarried men and unmarried women are equal.
Hence, the number of unmarried men is half of 230, i.e. 115.
As well as the number of unmarried women is another half of 230, i.e. 115.
Next, we know that 115 unmarried men represent 20% of all men.
Hence, the number of all men is 5 times 115, i.e. 575.
We also know that 115 unmarried women represent 25% of all women.
Hence, the number of all women is 4 times 115, i.e. 460.
Thus, the total number of employees is 575+460 = 1035.
The percentage of women is  =  = 0.444444... = 44.4444...%.
Solved (without using either equations).
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4-th or 5th grade level.
One or two years before they start learning equations.
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