Chapter 1.3, Problem 19Q

a.

To determine

To calculate:

Total hours after painting are the total costs same at both studios.

Answer to Problem 19Q

Total hours after painting are the total costs same at both studios is $3hours$ .

Explanation of Solution

Given information:

There are two studio $A$ and studio $B$ . The total cost is the cost of the piece plus an hourly studio fee.

Calculation:

Let consider,

  $x=$ Total cost.

  $y=$ the number of hours.

It is given that, total cost is the cost of the piece of pottery plus the number of hours multiplied by an hourly studio fee.

Now put the values,

For studio $A$ :

  $y=8x+\mathrm{10...}\left(1\right)$

For studio $B$ :

  $y=6x+\mathrm{16...}\left(2\right)$

Now equate and solve for $x$

  $\begin{array}{l}8x+10=6x+16\\ 8x-6x=16-10\\ 2x=6\\ x=\frac{6}{2}\\ x=3hours\end{array}$

b.

To determine

To calculate:

Affect in part a after Studio $B$ increases the hourly studio fee by $\$2$ .

Answer to Problem 19Q

The costs of both studios will never be the same, the cost of studio $B$ will always be higher than the cost of studio $A$

Explanation of Solution

Given information:

Studio $B$ increases the hourly studio fee by $\$2$ .

Calculation:

It is given that,

For studio $A$ :

  $y=8x+\mathrm{10...}\left(i\right)$

For studio $B$ :

  $\begin{array}{l}y=\left(6+2\right)x+16\\ y=8x+\mathrm{16...}\left(ii\right)\end{array}$

Now equat equation $A$ and $B$ and now aolve for $x$ ,

  $\begin{array}{l}8x+10=8x+16\\ 10=16\end{array}$

Thus, $10=16$ is not true.

So system has no solution.