Question

the table represents the time it took Bill to complete sets of math problems. Which equation represents this relationship?

time (in minutes) Number of Problems in set
30 36
40 48
50 60
60 72

y = 1.2x

y = 12x

y = x + 12

y = x + 1.2

Answer 1

To find the equation that represents the relationship between time (in minutes) and the number of problems in the set, we can look for a pattern in the provided data points:

- When time is 30 minutes, the number of problems is 36.
- When time is 40 minutes, the number of problems is 48.
- When time is 50 minutes, the number of problems is 60.
- When time is 60 minutes, the number of problems is 72.

We notice the increase in the number of problems as the time increases. To find the rate of change, we can calculate the increase in problems per minute:

1. From 30 to 40 minutes:
- Increase in problems = 48 - 36 = 12
- Time increase = 40 - 30 = 10 minutes
- Rate = 12 problems / 10 minutes = 1.2 problems per minute

2. From 40 to 50 minutes:
- Increase in problems = 60 - 48 = 12
- Time increase = 50 - 40 = 10 minutes
- Rate = 12 problems / 10 minutes = 1.2 problems per minute

3. From 50 to 60 minutes:
- Increase in problems = 72 - 60 = 12
- Time increase = 60 - 50 = 10 minutes
- Rate = 12 problems / 10 minutes = 1.2 problems per minute

The consistent increase of 1.2 problems per minute suggests a linear relationship can be expressed with the equation:

\( y = 1.2x \)

Where:
- \( y \) is the number of problems,
- \( x \) is the time in minutes.

So, the correct equation that represents the relationship between time and the number of problems is:

**\( y = 1.2x \)**.