Yesterday, Selma read 75 pages of her book. If she reads at a pace of 2 pages per minute today, which table shows only viable solutions for the total number of pages she has read, [tex]$y$[/tex], after [tex]$x$[/tex] minutes have elapsed?
Selma's Reading
| Minutes of Reading ([tex]$x$[/tex]) | Total Pages Read ([tex]$y$[/tex]) |
|---|---|
| 2 | 79 |
| 14 | |
Answer (1)
Establish the equation: y = 75 + 2 x , where y is the total pages read and x is the minutes of reading.
Substitute x = 2 into the equation: y = 75 + 2 ( 2 ) = 79 .
Substitute x = 14 into the equation: y = 75 + 2 ( 14 ) = 103 .
The total pages read after 14 minutes is 103 .
Explanation
Problem Analysis Let's analyze the problem. Selma read 75 pages yesterday and reads 2 pages per minute today. We want to find the total number of pages she has read, y , after x minutes today.
Equation Setup The total number of pages read, y , can be expressed as a function of the number of minutes, x , by the equation: y = 75 + 2 x where 75 is the number of pages read yesterday, and 2 x is the number of pages read today after x minutes.
Calculate y for x=2 Now, let's substitute x = 2 into the equation to find the corresponding y value: y = 75 + 2 ( 2 ) = 75 + 4 = 79 So, after 2 minutes, Selma has read a total of 79 pages.
Calculate y for x=14 Next, let's substitute x = 14 into the equation to find the corresponding y value: y = 75 + 2 ( 14 ) = 75 + 28 = 103 So, after 14 minutes, Selma has read a total of 103 pages.
Final Table Therefore, the table showing viable solutions for the total number of pages Selma has read, y , after x minutes is:
Minutes of Reading ( x )
Total Pages Read ( y )
2
79
14
103
Examples
Understanding how the number of pages read accumulates over time can be applied to various scenarios. For example, if you are tracking the progress of a project, you can use a similar linear equation to model the amount of work completed over time. If you know you start with 75 tasks already done and you complete 2 tasks per day, you can predict how many tasks will be completed after a certain number of days. This helps in project management and planning.
