Chapter SH, Problem 8.10MPS

(a)

To determine

To calculate: To write the system of equations to represent the situation

Answer to Problem 8.10MPS

System of equations is $3x+2y=15$ and $2x+4y=16$

Explanation of Solution

Given information:E spent $\$15$ for $3$ magazines and $2$ puzzle books. At the same store, C spent $\$16$ for $2$ magazines and $4$ puzzle books

Calculation:

Let the cost of one magazine be $x$

Let the cost of one puzzle book be $y$

Given that E spent $\$15$ for $3$ magazines and $2$ puzzle books.

Thus,

  $3x+2y=15$

Also, given that C spent $\$16$ for $2$ magazines and $4$ puzzle books

  $2x+4y=16$

Hence System of equation is given as

  $\begin{array}{l}3x+2y=15\\ 2x+4y=16\end{array}$

Conclusion:

Hence, system of equations is $3x+2y=15$ and $2x+4y=16$

(b)

To determine

To calculate: To solve the system of equations by graphing

Answer to Problem 8.10MPS

Solutions of system of equations is $\left(3.5,2.25\right)$

Cost of one magazine is $\$3.5$ and cost of one puzzle book is $\$2.25$

Explanation of Solution

Given information:System of equations are $3x+2y=15$ and $2x+4y=16$

Formula Used:

The point of intersection of two lines is the solution of the system of linear equations

Calculation:

System of equation is given as

  $\begin{array}{l}3x+2y=15\\ 2x+4y=16\end{array}$

Solving $3x+2y=15$

When $x=0$

  $\begin{array}{l}3\left(0\right)+2y=15\\ 2y=15\\ y=7.5\end{array}$

When $y=0$

  $\begin{array}{l}3x+2\left(0\right)=15\\ 3x=15\\ x=5\end{array}$

Solution of the equation are $\left(0,7.5\right),\left(5,0\right)$

Solving $2x+4y=16$

When $x=0$

  $\begin{array}{l}2\left(0\right)+4y=16\\ 4y=16\\ y=4\end{array}$

When $y=0$

  $\begin{array}{l}2x+4\left(0\right)=16\\ 2x=16\\ x=8\end{array}$

Solution of the equation are $\left(0,4\right),\left(8,0\right)$

Plotting the above points on graph,

From the graph, the lines intersect at point $\left(3.5,2.25\right)$

Thus, solution is $\left(3.5,2.25\right)$

Therefore, Cost of one magazine is $\$3.5$ and cost of one puzzle book is $\$2.25$

Conclusion:

Hence, solutions of system of equations is $\left(3.5,2.25\right)$