Chapter 6.1, Problem 25PPS

a.

To determine

Calculate the equation for the number of tickets each person has sold.

Answer to Problem 25PPS

The two equation are $y=20x+53andy=30x+22$ .

Explanation of Solution

Given:

It is given in the question that The person A sold $22$ and then sold $30$ per day after that, Jen sold $53$ on Monday and then sold $20$ per day after that .

Concept Used:

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

Calculation: Let y represents the number of tickets sold.

Let x represents the number of days.

Now, the equation for the the person A is : $y=30x+22$

And the equation for the Jen is : $y=20x+53$

Conclusion:

The two equation are $y=20x+53andy=30x+22$ .

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, $y=20x+53andy=30x+22$ .

Graph:

Interpretation: Here, put the both equation $y=20x+53andy=30x+22$ in the graphing calculator, it gives the required graph.

In the above graph, it can be easily seen that the two graph intersect at $(3.1,115)$ .

c.

To determine

Find the solution of the two equations. Check it.

Answer to Problem 25PPS

The person A will have sold $3$ more tickets.

Explanation of Solution

Given:

It is given in the question that the two graph gives the solution is $(3.1,115)$ .

Concept Used:

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

Calculation: Here, the solution is $(3.1,115)$ .To check the answer enter it into the both equation.

  $\begin{array}{l}y=20x+53\\ 115=20(3.1)+53\\ 115=62+53\\ 115=115\end{array}$

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

  $\begin{array}{l}y=30x+22\\ 115=30(3.1)+22\\ 115=93+22\\ 115=115\end{array}$

So, it is a solution for the second equation.

Hence, After about $3$ days, The person A will have sold more tickets.

Conclusion:

The person A will have sold $3$ more tickets.