Question

To mail the envelope first class do US post office charges $.39 for the 1st ounce and $.22 for each additional ounce . use inequality to find the maximum number of whole ounce of that can be mailed for $7.24

Answer 1

Let N be the total amount of whole ounces that are mailed.

Since mailing the first ounce has a cost of $0.39, then there will be N-1 ounces charged for $0.22 each.

The total cost of mailing N ounces will be:

`0.39+0.22*(N-1)`

If that cost cannot exceed $7.24, then:

`0.39+0.22*(N-1)\le7.24`

Solve the inequality for N:

`\begin{gathered} \Rightarrow0.22*(N-1)\le7.24-0.39 \\ \Rightarrow0.22N-0.22\le6.85 \\ \Rightarrow0.22N\le6.85+0.22 \\ \Rightarrow0.22N\le7.07 \\ \Rightarrow N\le(7.07)/(0.22) \\ \Rightarrow N\le32.136\ldots \end{gathered}`

Since N must be a whole number, the maximum value of N that satisfies the inequality is 32.

Therefore, the maximum number of whole ounces that can be mailed for $7.24 is:

`32`