Question

Nora and Lila are reading the same novel for book club. Nora is on page 128 and plans to read 8 pages per day until the next club meeting. Lila
is on page 102 and plans to read 12 pages per day until the next club meeting.

After how many days of reading will Nora and Lila be on the same page of the book? What page will they be on?

Answer 1

Answer:

- They will be on the same page after 6.5 days or $6\frac{1}{2}$ days.

- They will be on page 180.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

You know that Nora plans to read 8 pages per day until the next club meeting and she is on page 128.

With this information you can write the following equation of the line in Slope-Intercept form to represent the number of the page "y" she will be on after "x" days:

$y=8x+128$

Know that Lila is on page 102 and plans to read 12 pages per day until the next club meeting, you can write this linear equation that represent the number of the page "y" she will be on after "x" days:

$y=12x+102$

Since they will be on the same page after "x" days, make both equations equal and solve for "x":

$8x+128=12x+102\\\\26=4x\\\\x=6.5$

Substitute that value into any original equation the same page they will be on after 6.5 days (or $6\frac{1}{2}$ days):

$y=12(6.5)+102\\\\y=180$