SOLUTION: A survey of 900 Americans found that 680 had confidence in the economy. If 80% of the women and 70% of the men surveyed expressed confidence in the economy then how many men were s

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Question 202852: A survey of 900 Americans found that 680 had confidence in the economy. If 80% of the women and 70% of the men surveyed expressed confidence in the economy then how many men were surveyed?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A survey of 900 Americans found that 680 had confidence in the economy. If 80% of the women and 70% of the men surveyed expressed confidence in the economy then how many men were surveyed?

Let W = the number of women 
Let M = the number of men

>>...A survey of 900 Americans...<<

           (number of women) + (number of men) = (980 people)

                    W        +          M       = 980

>>...680 had confidence in the economy...<<
>>...80% of the women and 70% of the men...expressed confidence...<<

(80% of the number of women) + (70% of the number of men) = (680 people) 

            .80W             +             .70M           =  680 

So we have the system:

system%28W+%2B+M+=+900%2C.80W+%2B+.70M+=+680%29

Multiply the second equation through by 10 to remove decimals:

system%28W+%2B+M+=+900%2C8W+%2B+7M+=+6800%29

Solve the first equation for one of the letters, I'll pick M.

W%2BM=900

subtract W from both sides

M+=+900-W

Substitute %28900-W%29 for M in 

8W+%2B+7M+=+6800%29

8W+%2B+7%28900-W%29+=+6800%29

8W+%2B+6300-7W=6800

W%2B6300=6800

Add -6300 to both sides:

W=500

So there were 500 women. Substituting 500 for W in

M+=+900-W

M+=+900-500

M+=+400

So there were 400 men.

Edwin