Question

A box of pencils is 5 1/4 inches wide. Seven pencils, laid side by side, take up 2 5/8 inches of the width. How many inches of the width of the box is not taken up by pencils? Show your reasoning. All the pencils have the same width. How wide is each pencil? Show your reasoning.

Answer 1

Answer: Width of box is not taken up by pencils =
`2\frac58\text{ inches}`

Width of each pencil
`=\frac38\text{ inches}`

Explanation:

Given: Width of pencil box =
`5\frac14\text{ inches}=(21)/(4)\text{ inches}`

Width of seven pencils =
`2\frac58\text{ inches}=(16+5)/(8)\text{ inches}=(21)/(8)\text{ inches}`

Width of box is not taken up by pencils = Width of pencil box - Width of seven pencils

`\left \{ {{y=2} \atop {x=2}} \right. (21)/(4)-(21)/(8)\\\\=(21*2-21)/(8)\\\\=(21)/(8)\text{ inches}=2\frac58\text{ inches}`

Width of box is not taken up by pencils =
`2\frac58\text{ inches}`

Width of each pencil = (Width of seven pencils ) ÷ 7

`=(21)/(8)/7\\\\=(21)/(8)*\frac17\\\\=\frac38\text{ inches}`

Width of each pencil
`=\frac38\text{ inches}`