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QA survey of 900 Americans found that 680 had confidence in the economy

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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#1ZoeyAnswered at 2013-03-11 19:53:54
Let W = the number of women Let M = the number of men
#2MoketeAnswered at 2013-03-11 19:54:52
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? <pre><font size = 4 color = "indigo"><b> Let W = the number of women Let M = the number of men </pre></font></b> >>...A survey of 900 Americans...<< <pre><font size = 4 color = "indigo"><b> (number of women) + (number of men) = (980 people) W + M = 980 </pre></font></b> >>...680 had confidence in the economy...<< >>...80% of the women and 70% of the men...expressed confidence...<< <pre><font size = 4 color = "indigo"><b> (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>
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