Chapter 6.1, Problem 9CYU

a.

To determine

Find the equation to represent the pages that each boy has read.

Answer to Problem 9CYU

The two equation are $y=20x+35andy=10x+85$ .

Explanation of Solution

Given:

It is given in the question that Alberto read $35$ pages with $20$ pages each day and Ashanti read $85$ pages with $10$ pages each day.

Concept Used:

In this, use the concept of linear equations by understanding the correct variable and constant .

Calculation:

Let y represents the number of pages read.

Let x represents the number of days.

Now, the equation for the Alberto is : $y=20x+35$

And the equation for the Ashanti is : $y=10x+85$

Conclusion:

The two equation are $y=20x+35andy=10x+85$ .

b.

To determine

Draw the graph of the equation.

Explanation of Solution

Given:

It is given in the question that the given two equation are, $y=20x+35andy=10x+85$

Graph:

Interpretation: Here, put the both equation $y=20x+35andy=10x+85$ in the graphing calculator, it gives the required graph.

In the above graph, it can be easily seen that the two graph intersect at $(5,135)$ .

c.

To determine

Find the time at which Alberto has read more pages than Ashanti.check it.

Answer to Problem 9CYU

Alberto will have read more pages than Ashanti after $5$ days.

Explanation of Solution

Given:

It is given in the question that the two graph gives the solution of $(5,135)$ .

Concept Used:

In this, use the concept of linear equations by understanding the correct variable and constant .

Calculation: Here, the solution is $(5,135)$ .To check the answer enter it into the both equation.

  $\begin{array}{l}y=20x+35\\ 135=20(5)+35\\ 135=100+35\\ 135=135\end{array}$

So, it is a solution for the first equation. Now check the second equation.

  $\begin{array}{l}y=10x+85\\ 135=10(5)+85\\ 135=50+85\\ 135=135\end{array}$

So, it is a solution for the second equation.

Hence, Alberto will have read more pages than Ashanti after $5$ days.

Conclusion:

Alberto will have read more pages than Ashanti after $5$ days.