Question

Jose and Gavin are reading the same book. At the beginning of the month, Jose was

on page 10 and Gavin was on page 37. Jose will read 17 pages per day and Gavin will

read 14 pages per day. Let J represent the page of the book that Jose is on at the end

oft days into the month, and let G represent the page of the book that Gavin is on at

the end oft days into the month. Write an equation for each situation, in terms of t,

and determine what page Jose and Gavin will be on on the day they are both on the

same page.

Answer 1

Using linear functions, it is found that:

• Jose's equation is: $J = 17x + 10$.

• Gavin's equation is: $G = 14x + 37$.

• They will be on the same page on the 9th day.

Linear function:

A linear function is modeled by:

$y = mx + b$

In which:

• m is the slope, which is the rate of change.

• b is the y-intercept, which is the value of y when x = 0.

Jose:

• Initially, he was on page 10, hence $b = 10$.

• He reads 17 pages per day, hence $m = 17$.

• Hence, Jose's equation is: $J = 17x + 10$.

Gavin:

• Initially, he was on page 37, hence $b = 37$.

• He reads 14 pages per day, hence $m = 14$.

• Hence, Gavin's equation is: $G = 14x + 37$.

The day they will both be on the same page is x for which:

$J = G$

Hence:

$17x + 10 = 14x + 37$

$3x = 27$

$x = \frac{27}{3}$

$x = 9$

They will be on the same page on the 9th day.

To learn more about linear functions, you can take a look at https://brainly.com/question/16302622