Question 29192
Sometimes it helps to think backwards...<br>
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".
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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: {{{m+w=2000}}}
The problem also tells us that 70% of those 2000 are women, thus: {{{.70*2000=1400}}} 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:
{{{.4m+.8w=1400}}}
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We now have two equations and can solve for both variables. Using substitution we can rewrite Equation 1 as:
{{{m=2000-w}}}
So we can substitute for m in equation 2 with 2000-w and write:
{{{.4(2000-w)+.8w=1400}}} Distribute:
{{{800-.4w+.8w=1400}}}Rearrange:
{{{.4w=600}}}Divide by .4
{{{w=1500}}}
So m=2000-1500=500.  500 employees at Men's Mercantile and 1500 at Women's Wear.