Question

Steel bars shrink 8% when cooled from furnace temperature to room temperature. If a cooled steel bar is 46 in. long, how long was it when it was formed?The steel bar was __ in. long when it was formed.(Round to the nearest whole number as needed.)

Answer 1

50 inches

Explanation:

Let the length of the steel bar when it was formed = y

Steel bars shrink ​8% when cooled from furnace temperature to room temperature.

`\begin{gathered} \text{Room Temperature Length}=(100-8)\%\text{ of y} \\ =92\%y \\ =0.92y \end{gathered}`

Given that a cooled steel bar is 46 in.​ long, then:

`0.92y=46`

Divide both sides by 0.92.

`\begin{gathered} (0.92y)/(0.92)=(46)/(0.92) \\ y=50\;in. \end{gathered}`

The steel bar was 50 in. long when it was formed.