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,

`(50)/(80)=(6)/(x),\\ \\x=(80\cdot 6)/(50)=9.6\ yards.`

2. 50 pairs -- 6 yards,

100 pairs -- x yards.

Mathematically,

`(50)/(100)=(6)/(x),\\ \\x=(100\cdot 6)/(50)=12\ yards.`

3. 50 pairs -- 6 yards,

120 pairs -- x yards.

Mathematically,

`(50)/(120)=(6)/(x),\\ \\x=(120\cdot 6)/(50)=14.4\ yards.`

4. 50 pairs -- 6 yards,

140 pairs -- x yards.

Mathematically,

`(50)/(140)=(6)/(x),\\ \\x=(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.