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[Solved] Percents

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A survey of n people found that 60 percent preferred brand A. An additional x people were surveyed who all preferred brand A. Seventy percent of all the people surveyed preferred brand A. Find x in terms of n.

A)            B)           C)           D)  n         E)  3n

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The total number of people surveyed was \small n+x.  Since 70 percent of the total preferred brand A, that means \small 0.7(n+x) preferred brand A. However, 60 percent of the \small n  people and all of the \small x people preferred brand A. So, \small 0.6n+x preferred brand A. Therefore, \small 0.7(n+x) must equal \small 0.6n+x. So we have

\small 0.7n+0.7x=0.6n+x

\small 0.1n=0.3x

\small \Rightarrow x=\frac{n}{3}

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