Question

Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices.

Josiah’s Music
Sample 1
Sample 2
R & B
5
R & B
4
Pop
4
Pop
3
Classical
3
Classical
5
Jazz
2
Jazz
4
Rock
6
Rock
4

Josiah’s work:

StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x.
He should have found the average of the 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 times 75 = 1,500.

Answer 1

The true statements are:

• He should have found the average of the 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.
• He should have multiplied the numerator and denominator by 75, not 30, because 20 × 75 = 1500.

Explanation:

Given table displaying the counts of how many songs of each genre were played in an hour from Josiah's MP3 player:

`\begin{array}l\cline{1-4}\vphantom{\frac12}\sf Sample \;1&\phantom{www} &\sf Sample\;2&\phantom{www} \\\cline{1-4}\vphantom{\frac12}\textsf{R\&B} &5 & \textsf{R\&B} & 4\\\cline{1-4}\vphantom{\frac12}\sf Pop & 4 &\sf Pop & 3\\\cline{1-4}\vphantom{\frac12}\sf Classical & 3 & \sf Classical & 5\\\cline{1-4}\vphantom{\frac12}\sf Jazz & 2 & \sf Jazz & 4\\\cline{1-4}\vphantom{\frac12}\sf Rock & 6 & \sf Rock & 4\\\cline{1-4}\end{array}`

The total number of songs in Sample 1 is 20, of which 6 are rock songs.

The total number of songs in Sample 2 is 20, of which 4 are rock songs.

Josiah's work to predict the number of rock songs he has on his MP3 player given he has a total of 1,500 songs on his player:

`(10)/(20)=(x)/(1500)`

`(10 * 30)/(20 * 30)=(x)/(1500)`

`300=x`

The total number of rock songs from both samples is 10. So there are 10 rock songs from a total sample of 40 songs.

As Josiah used a total sample of 20 songs in his calculations, he should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

Looking at Josiah's calculations, he did not multiply the numerator and denominator by the correct number to equal 1,500. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.

The correct work is as follows:

`(5)/(20)=(x)/(1500)`

`(5* 75)/(20 * 75)=(x)/(1500)`

`375=x`

Therefore, the number of predicted rock songs on Josiah's MP3 player is 375.

Therefore, the true statements about his solution are:

• He should have found the average of the 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.
• He should have multiplied the numerator and denominator by 75, not 30, because 20 × 75 = 1500.