Jonathan practices the piano 658 minutes in 2 weeks. If *t* represents the total time he practices for any number of days, *d*, write a proportional equation for *t* in terms of *d* that matches the context.

To find a proportional equation that represents the total time \( t \) Jonathan practices in terms of the number of days \( d \), we need to determine the average time he practices per day.

First, we know:
- Jonathan practices for a total of 658 minutes in 2 weeks.
- There are 14 days in 2 weeks.

The average practice time per day is:
\[
\text{Average practice time per day} = \frac{658 \text{ minutes}}{14 \text{ days}} = 47 \text{ minutes per day}
\]

Using this information, we can write a proportional equation where \( t \) (total practice time in minutes) is proportional to \( d \) (number of days):

\[
t = 47d
\]

So, the equation \( t = 47d \) accurately represents the total time Jonathan practices in terms of the number of days.

Would you like more details or have any questions?

Here are 8 related questions to expand your understanding:

1. How would the equation change if Jonathan practiced for 720 minutes in 2 weeks?
2. What would the equation be if he practiced for a different number of days, say in 10 days?
3. How can you use this equation to find out how many days it takes Jonathan to practice a certain amount of minutes, say 235 minutes?
4. If Jonathan decides to increase his daily practice time by 10%, what would the new proportional equation be?
5. How can you graph this equation on a coordinate plane?
6. What is the slope of the line representing the equation \( t = 47d \)?
7. How does this equation change if Jonathan practices less on weekends than on weekdays?
8. How would you modify the equation if Jonathan takes 1 day off every week?

**Tip:** Understanding proportional relationships helps in solving problems related to direct variation, where one quantity changes directly as another.

Understand Jonathan's practice time proportional equation where t represents total practice time and d represents the number of days. Learn how to calculate practice time for different periods and apply proportional relationships in daily routines. Suitable for Grades 7-9 students.

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