Chapter 5.6, Problem 13IP

To determine

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

Answer to Problem 13IP

The complete table is given below:

Length of Ribbon $\left(\text{yd}\right)$	$5$	$7.5$	$15$	$25$
Total cost $\left(\$\right)$	$2$	$3$	$6$	$10$

Explanation of Solution

Given information:The table is given as:

Length of Ribbon $\left(\text{yd}\right)$	$5$	$7.5$	$?$	$25$
Total cost $\left(\$\right)$	$2$	$?$	$6$	$?$

Calculation:

It is given that the length of ribbon is proportional to the total cost, this means the constant of proportionality is constant for each value.

As given the total cost is $\$2$ for $5\text{yd}$ of length of ribbon. So, the total cost for $1\text{yd}$ of length of ribbon is:

  $\frac{\$2}{5}=\$0.4$

So, the constant of proportionality is $0.4$ it means that the cost of each yard length of ribbon is $\$0.4$ .

The formula for the total cost for $l\text{yd}$ length of ribbon is:

  $C=\$0.4l$

Substitute $7.5$ for $l$ in the formula for total cost.

  $\begin{array}{c}C=\$0.4\times 7.5\\ =\$3\end{array}$

So, the total cost for $7.5\text{yd}$ of ribbon is $\$3$ .

Substitute $25$ for $l$ in the formula for total cost.

  $\begin{array}{c}\text{C}=\$0.4\times 25\\ =\$10\end{array}$

So, the total cost for $25\text{yd}$ of ribbon is $\$10$ .

Substitute $\$6$ for C in the formula for total cost.

  $\begin{array}{c}\$6=\$0.4l\\ \frac{\$6}{\$0.4}=l\\ l=15\text{yd}\end{array}$

So, the number of yards of length of ribbon for cost of $\$6$ is $15$ .

Therefore, the complete table is shown below:

Length of Ribbon $\left(\text{yd}\right)$	$5$	$7.5$	$15$	$25$
Total cost $\left(\$\right)$	$2$	$3$	$6$	$10$