Question

A factory produces 5-packs of pencils. To be within the weight specifications, a pack of 5 pencils should weigh between 60 grams and 95 grams. Each package has a mass of 15 grams. Enter a compound inequality to represent the mass of a single pencil in a pack. Can each pencil have a mass of 10.5 grams? Complete the explanation. The compound inequality can be entered as Each pencil has a mass between 9 and g., inclusive, so a pencil (select)y have a mass of 10.5 g.

Answer 1

We know that a pack of 5 pencils, including the package, has to be within 60 grams and 95 grams.

If P is the weight of each pencil and the package weights 15 grams, the weight of the pack is:

`5P+15`

Then, we can start by writing the inequality for the pack as:

`\begin{gathered} 60\le5P+15\le95 \\ 60-15\le5P\le95-15 \\ 45\le5P\le80 \\ (45)/(5)\le P\le(80)/(5) \\ 9\le P\le16 \end{gathered}`

Each pencil can weight between 9 and 16 grams inclusive, so a pencil can have a mass of 10.5 grams.