Question

From question: Montell is practicing his violin. He is able to play six songs for every nine minutes he practices.*Picture has the table and other questions*

Answer 1

The complete table:

6 18 2 42

9 27 3 63

Step-by-step explanation:

We know that for every 9 minutes Montell practices he is able to play 6 songs. This means that the ratio between the number of minutes practices to the number of songs played is

`\frac{\min}{\text{song}}=(9)/(6)`

Therefore, if we want to solve for minutes plated, we just multiply both sides by 'song' to get

`song*\frac{\min}{\text{song}}=(9)/(6)*\text{song}`

which gives

`min=(9)/(6)*\text{song}`

This means the number of minutes practised is 9/6 of the number of songs played.

Now 9/ 6 can be simplfied by dividing both the numerator and the denominator by 3 to get

`(9/3)/(6/3)=(3)/(2)`

therefore, we have

`min=(3)/(2)*\text{song}`

Now we are ready to fill the table.

If Montell plays 18 songs then we have

`\min =(3)/(2)*18`
`\min =27`

the minutes practised is 27 for 18 songs.

If Montell practices for 3 minutes then we have

`3=(3)/(2)*\text{song}`

then the value of song must be song = 2, since

`\begin{gathered} 3=(3)/(2)*2 \\ 3=3 \end{gathered}`

Hence, for 3 minutes of practice, Montell sings 2 songs.

Now for 42 songs, the number of minutes played would be

`\min =(3)/(2)*42`

which simplifies to give

`\min =63`

Hence, for 42 songs played, the practice time is 63 minutes.

To summerise, the complete table would be

songs 6 18 2 42

minutes 9 27 3 63