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?

Answer 1

The compound inequality will be:  $9\leq x\leq 16$, where $x$ is the mass of a single pencil and each pencil can have a mass of 10.5 grams.

Explanation

Suppose, the mass of a single pencil in the pack is  $x$ gram.

So, the total mass of 5 pencils will be:  $5x$ grams.

Each package has a mass of 15 grams. So, the total weight of the pack of 5 pencils $=(5x+15)$ grams.

To be within the weight specifications, a pack of 5 pencils should weigh between 60 grams and 95 grams. So, the compound inequality will be..........

$60\leq 5x+15\leq 95\\ \\ 60-15\leq 5x+15-15\leq 95-15\\ \\ 45\leq 5x\leq 80\\ \\ \frac{45}{5}\leq \frac{5x}{5}\leq \frac{80}{5}\\ \\ 9\leq x\leq 16$

So, the compound inequality to represent the mass of a single pencil in a pack will be:  $9\leq x\leq 16$, where $x$ is the mass of a single pencil.

• As 10.5 grams lies inside the interval $9\leq x\leq 16$ , so each pencil can have a mass of 10.5 grams.

Answer 2

Divide the weight variance of a pack by 5, yielding
12 to 19 grams.
Then a single pencil can be between 12 < pencil < 19 grams.
Therefore each pencil cannot have a mass of 10.5 grams.