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

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.

Answer 2

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.

Step-by-step 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\\ \\ (45)/(5)\leq (5x)/(5)\leq (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.