Question

A sneaker company can make 50 pairs of sneakers for every 6 yards of material. Make a table to show the relation between material needed for 80, 100, 120, 140 pairs of snaekers.
Then state the domain and range and graph this relation.
Create a graph based on the table.

Answer 1

A sneaker company can make 50 pairs of sneakers for every 6 yards of material.

Then in each case you can consider proportion.

1. 50 pairs -- 6 yards,

80 pairs -- x yards.

Mathematically,

$\dfrac{50}{80}=\dfrac{6}{x},\\ \\x=\dfrac{80\cdot 6}{50}=9.6\ yards.$

2. 50 pairs -- 6 yards,

100 pairs -- x yards.

Mathematically,

$\dfrac{50}{100}=\dfrac{6}{x},\\ \\x=\dfrac{100\cdot 6}{50}=12\ yards.$

3. 50 pairs -- 6 yards,

120 pairs -- x yards.

Mathematically,

$\dfrac{50}{120}=\dfrac{6}{x},\\ \\x=\dfrac{120\cdot 6}{50}=14.4\ yards.$

4. 50 pairs -- 6 yards,

140 pairs -- x yards.

Mathematically,

$\dfrac{50}{140}=\dfrac{6}{x},\\ \\x=\dfrac{140\cdot 6}{50}=16.8\ yards.$

Thus, the table is

$\begin{array}{cc}\text{Pairs}&\text{Yards}\\50&6\\80&9.6\\100&12\\120&14.4\\140&16.8\end{array}$

The domain of the relation is the set $\{50,80,100,120,140\}$ and the range of the relation is $\{6,9.6,12,14.4,16.8\}.$See attached diagram for the graph of the relation.