Chapter 8.5, Problem 22STP

(a)

To determine

To write:an equation to find the cost of any number of admission tickets.

Answer to Problem 22STP

Therefore, the equation is $y=12.75x$

Explanation of Solution

Given: one ticket costs $\$12.75$ .

Calculation:

Consider that the cost of admission varies directly with number of tickets purchased. And, the cost of $1$ tickets is $\$12.75$

The cost is denoted $y$ and number of tickets purchased is denoted by $x$

Now, if there is direct variation then there is some constant variable $k$ such that satisfies the equation: $y=kx$

So, put the value of $x=1$ and $y=12.75$ in equation to find the value of $k$ .

  $12.75=1k$

Use $k$ to write an equation.

  $y=12.75x$

Therefore, the equation is $y=12.75x$

Conclusion:

Therefore, the equation is $y=12.75x$

(b)

To determine

To find: the cost of $15$ tickets.

Answer to Problem 22STP

Therefore, the cost of $15$ tickets is $\$191.25$ .

Explanation of Solution

Calculation:

Now, in order to calculate the cost of $15$ tickets, put the value of $x=15$ in equation.

  $\begin{array}{l}y=12.75(15)\\ =191.25\end{array}$

Therefore, the cost of $15$ tickets is $\$191.25$ .

Conclusion:

The result is:

Therefore, the cost of $15$ tickets is $\$191.25$ .