Question

Parker and Grayson are reading the same book. At the beginning of the month, Parker was on page 50 and Grayson was on page 8. Parker will read 11 pages per day and Grayson will read 18 pages per day. Let PP represent the page of the book that Parker is on at the end of tt days into the month, and let GG represent the page of the book that Grayson is on at the end of tt days into the month. Write an equation for each situation, in terms of t,t, and determine what page Parker and Grayson will be on on the day they are both on the same page.

Answer 1

Answer:

Page 116

Step-by-step explanation:

Parker started on page 50 at t = 0 days, and he will read 11 pages per day. Therefore the page that Parker will be on after t days is:

P = 11t + 50

Grayson started on page 8 at t = 0 days, and he will read 18 pages per day. Therefore the page that Grayson will be on after t days is:

G = 18t + 8

To find the number of days, t, after which Parker and Grayson will be on the same page, set the two equations equal to each other and solve for t :

11t + 50 = 18t + 8

     -18t        -18t                                                        ( subtract 18t )

-7t + 50 = +8

      -50     -50                                                          ( subtract 50 )

       -7t  =  -42

       -7t =  -42

        -7        -7                                                          ( divide by -7 )

           t  = 6

Since both equation values are equal when t = 6, we know Parker and Grayson will be on the same page after 6 days.

Now find the page number both Parker and Grayson will be on at this time. You can plug t = 6 into either equation.

P  = 11(6) + 50 = 116

G  = 18(6) + 8 = 116

Parker and Grayson are both on page 116 after 6 days.

Final Answer:

P  = 11t + 50            G  = 18t + 8

Answer: Page 116