Chapter 5.6, Problem 14IP

To determine

To find: The missing values in the given table for a proportional relationship.

Answer to Problem 14IP

The complete table is given below:

Number of Tickets	$1$	$3$	$4$	$7$
Total cost $\left(\$\right)$	$6$	$18$	$24$	$42$

Explanation of Solution

Given information:The table is given as:

Number of Tickets	$1$	$3$	$?$	$?$
Total cost $\left(\$\right)$	$6$	$?$	$24$	$42$

Calculation:

As given the number of tickets is proportional to the total cost, this means the constant of proportionality is constant for each value.

As given the total cost is $\$6$ for $1$ ticket.The constant of proportionality is $6$ it means that the cost for each ticket is $\$6$ .

So, the total cost for $n$ ticketsis $C=\$6n$ .

Substitute $3$ for $n$ in the formula for total cost.

  $\begin{array}{c}C=\$6\times 3\\ =\$18\end{array}$

So, the total cost for $3$ ticketsis $\$3$ .

Substitute $\$24$ for Cin the formula for total cost.

  $\begin{array}{c}\$24=\$6n\\ n=\frac{\$24}{\$6}\\ n=4\end{array}$

So, the number of tickets for $\$24$ is $4$ .

Substitute $\$42$ for Cin the formula for total cost.

  $\begin{array}{c}\$42=\$6n\\ n=\frac{\$42}{\$6}\\ n=7\end{array}$

So, the number of tickets for $\$42$ is $7$ .

Therefore, the complete table is shown below:

Number of Tickets	$1$	$3$	$4$	$7$
Total cost $\left(\$\right)$	$6$	$18$	$24$	$42$