SOLUTION: Hello, I'm older but new at word problems. We are using labels x Per = Total to solve this word problem. Two clothing businesses are merged into one. At Men's Mercantile,

Question 29192: Hello,
I'm older but new at word problems. We are using labels x Per = Total to solve
this word problem.
Two clothing businesses are merged into one. At Men's Mercantile, 40% of the employees are women. At Women's Wear 80% are women. After the merger, 70% of the 2000 employees are women. How many employees were employed by each business before the merger?
Found 2 solutions by Paul, bmauger:
Answer by Paul(988) (Show Source): You can put this solution on YOUR website!
equation:
40x+80(2000-x)=70(2000)
40x+160000-80x=140000
-40x=-20000
x=500

2000-500=1500

For men its 500 and for women its 1500 .
Paul.
Answer by bmauger(101) (Show Source): You can put this solution on YOUR website!
Sometimes it helps to think backwards...

The question ultimately asks us how many employees were employed by each business. Since these are the values we're ultimately trying to solve for, we'll call the # working at Men's Mercantile "m" and the number at Women's Wear "w".

After the merger there are 2000 employees. Thus when you add the number working at Men's Mercantile "m" with "w" you get 2000. Or:
Equation 1:
The problem also tells us that 70% of those 2000 are women, thus: 1400 are women.
If 40% working at Men's Mercantile are women, then we can write the number of women at MM as 40% of m or .4 times m. We can also see that the number of women working at Women's Wear is .8w. When we add the numbers up we get:

We now have two equations and can solve for both variables. Using substitution we can rewrite Equation 1 as:

So we can substitute for m in equation 2 with 2000-w and write:
Distribute:
Rearrange:
Divide by .4

So m=2000-1500=500. 500 employees at Men's Mercantile and 1500 at Women's Wear.
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