Question

Two students are reading a novel. Ashley reads$10$ pages per day. Carly reads $8$ pages per day , but she started early and is already on page $40$. Write a system of equations to represent the situation, using $d$ for days and $p$ for pages.

Answer 1

Find the system of equations to represent the situation.

The linear equation with slope-intercept form is,

$y=ax+b$

Here $a$and $b$are the numbers.

Replace the variables $d$ for $x$ and $p$for $y$.

Here $p$represents pages and $d$represents days.

So rewrite the equation as follows.

$p=ad+b$

Since Ashley reads$10$ pages per day.

Substitute $a=10$and $b=0$in the linear equation.

$\begin{array}{rcl}p& =& \left(10\right)d+0\\ & \Rightarrow & p=10d\end{array}$

And Carly reads $8$ pages per day, but she started early and is already on page $40$.

Substitute $a=8$and $b=40$in the linear equation:

$\begin{array}{rcl}p& =& \left(8\right)d+40\\ & \Rightarrow & p=8d+40\end{array}$

Therefore, the system of equations will be $\begin{array}{rcl}\mathit{p}& \mathbf{=}& \mathbf{10}\mathit{d}\end{array}$ and $\begin{array}{rcl}\mathit{p}& \mathbf{=}& \mathbf{8}\mathit{d}\mathbf{+}\mathbf{40}\end{array}$.