Josiah tracked the number of songs…

Maths Questions

Josiah tracked the number of songs from each genre played in an hour on his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player and predicted the number of rock songs to be 300. Which statements about his solution are true? Check all that apply. Josiah’s Music Sample 1: R & B – 5, Pop – 4, Classical – 3, Jazz – 2, Rock – 6; Sample 2: R & B – 4, Pop – 3, Classical – 5, Jazz – 4, Rock – 4. Josiah’s work: 10/20 = x/1,500. 10×30/20×30=x/1,500. 300=x. He should have found the average number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20×75=1,500.

Answer

Josiah’s prediction of the number of rock songs on his MP3 player contained several inaccuracies. Firstly, he failed to average the counts of rock songs from his samples properly; he should have calculated the average to be 5 instead of relying on individual values. Furthermore, he used an incorrect multiplication factor of 30 in his proportion calculation, rather than the necessary factor of 75 to scale the data accurately to the total of 1,500 songs. The correct way to set up the proportion should have been 5/20 = x/1,500, which simplifies to 1/4 = x/1,500, giving x = 375 as the predicted number of rock songs in his collection.

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