Chapter 1.5, Problem 23E

a.

To determine

To calculate:

The literal equation in terms of $x$

Answer to Problem 23E

The formula in terms of $x$ is $\frac{C-60}{85}$ .

Explanation of Solution

Given information:

  $C=85x+60$

Calculation:

The given formula for total cost $C$ (in dollars) to participate in a ski club is:

  $C=85x+60$......................... (1)

Switch both sides as to get the formula for number of ski trips:

  $85x+60=C$

Subtract $60$ from both sides if equations:

  $\begin{array}{l}85x+60-60=C-60\\ 85x=C-60\end{array}$

Divide by $85$ :

  $\begin{array}{l}\frac{85}{85}x=\frac{C-60}{85}\\ x=\frac{C-60}{85}\end{array}$

b.

To determine

To calculate:

The number of ski trips for total cost of $\$315,\$485$

Answer to Problem 23E

The number of ski trips for total cost of $\$315$ and $\$485$ is $3$ and $5$ respectively.

Explanation of Solution

Given information:

  $\begin{array}{l}{C}_1=\$315\\ C_2=\$485\end{array}$

Calculation:

From the subpart (a):

The formula for number of ski trips is given as:

  $x=\frac{C-60}{85}$

Put the given data: $C_1=\$315,C_2=\$485$

  $\begin{array}{l}{x}_1=\frac{C_1-60}{85}=\frac{315-60}{85}=3\\ x_2=\frac{C_2-60}{85}=\frac{485-60}{85}=5\end{array}$