Chapter 4.1, Problem 33PPS

a

To determine

Cost of each article for which you pay a fee.

Answer to Problem 33PPS

The cost of each article is $ $2.75$ .

Explanation of Solution

Given:

Consider $25x$ is the cost of the magazine subscription.

And y is the cost of per article for which pay a fee.

Calculation:

According to given conditions,

  $\begin{array}{l}25x+5y=49.15\mathrm{...}(1)\\ 25x+8y=57.40\text{}\mathrm{...}(2)\end{array}$

Subtract first equation from second equation.

  $\begin{array}{l}25x+8y=57.40\text{}\mathrm{...}(2)\\ \underset{\_}{25x+5y=49.15}\mathrm{...}(1)\\ 0x+3y=8.25\end{array}$

Now, divide by 3 on both the sides,

  $\begin{array}{l}\frac{3y}{3}=\frac{8.25}{3}\\ y=2.75\end{array}$

b

To determine

Cost of magazine subscription.

Answer to Problem 33PPS

The Cost of magazine subscription $\$35.4$

Explanation of Solution

Given:

Consider $25x$ is the cost of the magazine subscription.

And y is the cost of per article for which pay a fee.

Calculation:

According to given condition,

  $\begin{array}{l}25x+5y=49.15\mathrm{...}(1)\\ 25x+8y=57.40\text{}\mathrm{...}(2)\end{array}$

Subtract first equation from second equation.

Subtract first equation from second equation.

  $\begin{array}{l}25x+8y=57.40\text{}\mathrm{...}(2)\\ \underset{\_}{25x+5y=49.15}\mathrm{...}(1)\\ 0x+3y=8.25\end{array}$

Now, divide by 3 on both the sides,

  $\begin{array}{l}\frac{3y}{3}=\frac{8.25}{3}\\ y=2.75\end{array}$

And when substitute it in first equation,

  $\begin{array}{l}25x+5\left(2.75\right)=49.15\\ 25x+13.75=49.15\\ 25x=49.15-13.75\\ 25x=35.4\end{array}$

Therefore the cost of the magazine subscription is $\$35.4$ .

And cost of per article for which pay a fee is $y=\$2.75$ .