Question

The cost of shipping a 25-lb. box with UPS is $25.50. If the weight, w, of the box may vary by no more than 3 pounds, what is the range of weights of a box that ships for $25.50?

Answer 1

`22\leq w\leq 28`

Explanation:

Let w represent weight of the box.

We have been given that the the cost of shipping a 25-lb. box with UPS is $25.50.

We will use tolerance formula to solve our given problem.

`|\text{Actual}-\text{Ideal}|\leq \text{Tolerence}`

`|w-25|\leq 3`

Using absolute inequality, if
`|u|\leq a`; then
`-a\leq u \leq a`

`-3\leq w-25\leq 3`

`-3+25\leq w-25+25\leq 3+25`

`22\leq w\leq 28`

Therefore, the range of weights of a box is
`22\leq w\leq 28` that ships for $25.50.

Answer 2

Let w represents the weight of the box .

It is given that , the weight, w, of the box may vary by no more than 3 pounds.

That is

`| w-25 | \leq  3`

`-3 \leq w-25 \leq  3`

Adding 25

`25-3 \leq  w  \leq  25+3 \\ 22 \leq  w \leq  28`

And that's the required range .