Question

Sven is trying to find the maximum amount of time he can spend practicing the five scales of piano music he is supposed to be working on. He has 60 minutes to practice piano and would like to spend at least 35 minutes playing songs instead of practicing scales. So, Sven sets up the following inequality, where t is the number of minutes he spends on each scale, and solves it.

Answer 1

He must spend no more that 25 minutes practising scales.

Explanation:

5t + 35 ≤ 60

5t ≤ 25

t ≤ 5.

So the maximum time for practising the scales is 5*5 = 25 minutes.

Answer 2

Sven should spend 5 minutes or less on each scale. Maximum times is 25 minutes.

Explanation:

Total time to practice piano = 60 minutes

He would like to spend at least 35 minutes playing songs instead of practicing scales.

Let t is the number of minutes he spends on each scale.

The time spend on 5 scales = 5t

Time for playing songs = 60 - 5t

It is given that he would like to spend at least 35 minutes playing songs instead of practicing scales. It means time for playing songs is greater than or equal to 35.

`60-5t\geq 35`

Subtract 60 from both sides.

`60-5t-60\geq 35-60`

`-5t\geq -25`

Divide both sides by -5. If an inequality is divided or multiplied by a negative number, then the sign of inequality is changed.

`t\leq 5`

Sven should spend 5 minutes or less on each scale.

The maximum value of t is 5, so the maximum time spend on practicing scales is

`\text{Maximum time}=5t\Rightarrow 5(5)=25`

Therefore, the maximum time is 25 minutes.