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?
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Let W = the number of women 
Let M = the number of men
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>>...A survey of 900 Americans...<<
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           (number of women) + (number of men) = (980 people)

                    W        +          M       = 980                    
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>>...680 had confidence in the economy...<<
>>...80% of the women and 70% of the men...expressed confidence...<<
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(80% of the number of women) + (70% of the number of men) = (680 people) 

            .80W             +             .70M           =  680 

So we have the system:

{{{system(W + M = 900,.80W + .70M = 680)}}}

Multiply the second equation through by 10 to remove decimals:

{{{system(W + M = 900,8W + 7M = 6800)}}}

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

{{{W+M=900}}}

subtract W from both sides

{{{M = 900-W}}}

Substitute {{{(900-W)}}} for {{{M}}} in 

{{{8W + 7M = 6800)}}}

{{{8W + 7(900-W) = 6800)}}}

{{{8W + 6300-7W=6800}}}

{{{W+6300=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</pre>