Chapter 5.6, Problem 15IP

To determine

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

Answer to Problem 15IP

The complete table is given below:

Boxes of Cat Food	$3$	$6$	$9$	$15$
Weight $\left(\text{lb}\right)$	$8$	$16$	$24$	$40$

Explanation of Solution

Given information:The table is given as:

Boxes of Cat Food	$?$	$6$	$9$	$15$
Weight $\left(\text{lb}\right)$	$8$	$16$	$?$	$?$

Calculation:

As given the boxes of cat food is proportional to the weight, this means the constant of proportionality is constant for each value.

As given the weight is $16\text{lb}$ for $6$ boxes of cat food. So, the constant of proportionality is:

  $\frac{16}{6}=\frac{8}{3}$

This means that the weight for each box of cat foodis $\frac{8}{3}\text{lb}$ .

So, the total weight for $n$ boxes of cat foodis $\text{W}=\frac{8}{3}n\text{lb}$ .

Substitute $9$ for $n$ in the formula for weight.

  $\begin{array}{c}\text{W}=\frac{8}{3}\times 9\text{lb}\\ =24\text{lb}\end{array}$

So, the weight for $9$ boxes of cat foodis $24\text{lb}$ .

Substitute $15$ for $n$ in the formula for weight.

  $\begin{array}{c}\text{W}=\frac{8}{3}\times 15\text{lb}\\ =40\text{lb}\end{array}$

So, the weight for $15$ boxes of cat food is $40\text{lb}$ .

Substitute $8\text{lb}$ for $\text{W}$ in the formula for weight.

  $\begin{array}{c}8\text{lb}=\frac{8}{3}n\text{lb}\\ n=\frac{8}{\frac{8}{3}}\\ n=3\end{array}$

So, the number of boxes for $8\text{lb}$ weight is $3$ .

Therefore, the complete table is shown below:

Boxes of Cat Food	$3$	$6$	$9$	$15$
Weight $\left(\text{lb}\right)$	$8$	$16$	$24$	$40$