SOLUTION: A survey of 700 people was conducted. Forty percent of the men surveyed supported the issue in question, while 70 percent of the women supported it. A total of 400 supported the is

Question 115242: A survey of 700 people was conducted. Forty percent of the men surveyed supported the issue in question, while 70 percent of the women supported it. A total of 400 supported the issue. How many more women than men were surveyed?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let M be the number of men in the survey and W be the number of women. Since 700 people were
surveyed we can say:
.
M + W = 700
.
Next you are told that 40% (0.4) of the men and 70% (0.7) of the women supported the issue
and that 400 people supported it. So we can also say:
.
0.4M + 0.7W = 400
.
Get rid of the decimals by multiplying both sides (all terms) of this equation by 10 to get:
.
4M + 7W = 4000
.
So now you have two equations to solve simultaneously:
.
+M + W = 700
4M +7W = 4000
.
You can use variable elimination. Multiply the top equation (both sides and all terms) by
-7 and the set of equations then becomes:
.
-7M - 7W = -4900
+4M + 7W = +4000
.
Add the columns vertically and the first column (-7M + 4M) becomes -3M. In the second
column the -7W cancels the +7W and the column has an answer of zero (or just a blank). On
the right side the -4900 and the +4000 add to give -900. So the result of adding the
two equations in columns is:
.
-3M = -900
.
Solve for M by dividing both sides of this equation by -3 and you get:
.
M = -900/-3 = 300
.
So the survey population contained 300 men. Since the total number of persons surveyed was
700, that means that the remaining 400 persons were women.
.
In summary ... 300 men and 400 women were surveyed.
.
Check. Does 40% of the men and 70% of the women total to 400? 40% of 300 is 120 and 70%
of 400 is 280 ... and 120 + 280 does equal 400. So the answer is correct.
.
Hope this helps you to understand the problem and one way of solving it.
.
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