Question

Gary needs 24 screws for every 2 chairs he builds.

Complete the table using equivalent ratios.
Number of chairs Number of screws
2 24
6
9

Answer 1

72 screws are required to make 6 chairs.

108 screws are required to make 9 chairs.

Explanation:

We are given the following in the question:

Gary needs 24 screws for every 2 chairs he builds.

We calculate the equivalent ratio to calculate number of screws required.

Ration of chairs to screws can be calculated as:

`\displaystyle\frac{\text{Number of chairs}}{\text{Number of screws}} = (2)/(24) = (1)/(12) = 1:12`

This can be interpreted hat 1 chair needs 12 screw.

We have to find number of screws required to make:

1. 6 chairs

Let x be the number of screws required to make 6 chairs, the we can write,

`\displaystyle(6)/(x) = (1)/(12)\\\\x = 6* 12 = 72`

72 screws are required to make 6 chairs.

2. 9 chairs

Let y be the number of screws required to make 9 chairs, the we can write,

`\displaystyle(9)/(y) = (1)/(12)\\\\y = 9* 12 = 108`

108 screws are required to make 9 chairs.

Answer 2

`\begin{array}{cc}\text{Nimber of chairs}&\text{Number of screws}\\ \\2&24\\6&72\\9&108\end{array}`

Explanation:

Gary needs 24 screws for every 2 chairs he builds.

Equivalent unit rate:

Gary needs 12 screws for each chair he builds.

Using this unit rate, we can state that

• Gary needs 72 screws for every 6 chairs he builds;
• Gary needs 108 screws for every 9 chairs he builds.

So, the table is

`\begin{array}{cc}\text{Nimber of chairs}&\text{Number of screws}\\ \\2&24\\6&72\\9&108\end{array}`