Chapter 8.10, Problem 15PPS

(a)

To determine

The system of equations which represent the given problem conditions

Answer to Problem 15PPS

The system of equations is:

  $\begin{array}{l}y=5x+50\\ y=-5x+90\end{array}$

Explanation of Solution

Given:

Two conditions given in problem:

Lings start out with $50$ baseball cards and plans to collect $5$ per month

Jonathon start out with $90$ baseball cards and plans to sell $5$ per month

Consider;

The number of baseball card: $y$

The number of months: $x$

Now, write the equations for two problem conditions:

  $y=5x+50$....... (1)

  $y=-5x+90$....... (2)

Conclusion:

Thus, the equation system is written as:

  $\begin{array}{l}y=5x+50\\ y=-5x+90\end{array}$ .

(b)

To determine

The solution of the system of equations with help of graphing method and its meaning is to be explained.

Answer to Problem 15PPS

The graphing method solution is:

  

It shows that after $\left(4\right)$ months, they will have the same number of cards $\left(70\right)$ .

Explanation of Solution

Given:

Two conditions given in problem:

Lings start out with $50$ baseball cards and plans to collect $5$ per month

Jonathon start out with $90$ baseball cards and plans to sell $5$ per month

To use the graphing method:

Consider;

The number of baseball card: $y$

The number of months: $x$

Now, write the equations for two problem conditions:

  $y=5x+50$....... (1)

  $y=-5x+90$....... (2)

Now, plot these two eqn. on graph which is shown by the following image:

  

The solution $\left(4,70\right)$ means that after $\left(4\right)$ months, they will have the same number of cards $\left(70\right)$ .

Conclusion:

So, the solution of the equation of system is $\left(4,70\right)$ with the graphing method.