Maths Olympiad Prep

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Algebra Difficulty 2.0 Junior Find the answer

Country music songs are added to a playlist so that now 40%40\% of the songs are Country. If the ratio of Hip Hop songs to Pop songs remains the same, what percentage of the total number of songs are now Hip Hop?

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since 40%40\% of the songs on the updated playlist are Country, then the remaining 100%−40%100\%-40\% or 60%60\% must be Hip Hop or Pop songs. Since the ratio of Hip Hop songs to Pop songs does not change, then 65%65\% of this remaining 60%60\% must be Hip Hop songs. Overall, this is 65%×60%=0.65×0.6=0.39=39%65\% \times 60\%=0.65 \times 0.6=0.39=39\% of the total number of songs on the playlist.

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