Question

To mail envelope first class the US post office charges $.34 for the 1st ounce and $.29 for each additional ounce. use an inequality to find the maximum number of whole Ounces that can be mailed for $3.33

Answer 1

Step 1: Given data

Cost for the first ounce = $0.34

Cost for each additional ounce = $0.29

Step 2:

Let the number of the whole Ounces that can be mailed for $3.33 = n

Step 4:

Write an inequality equation for the number of the whole Ounces that can be mailed for $3.33

Cost for the first ounce = $0.34

Cost for thr additional Ounces = (n - 1) x $0.29

The word maximum means greater than or equal to.

$\begin{gathered} 0.34\text{ + 0.29(n - 1) }\ge\text{ 3.33} \\ 0.34\text{ + 0.29n - 0.29 }\ge\text{ 3.33} \\ \text{collect like terms} \\ 0.29n\text{ }\ge\text{ 3.33 + 0.29 - 0.34} \\ 0.29n\text{ }\ge\text{ 3.28} \\ \text{Divide through by 0.29} \\ \frac{0.29n}{0.29}\text{ }\ge\text{ }\frac{3.28}{0.29} \\ n\text{ }\ge\text{ 11.3} \end{gathered}$

Final answer

The maximum number of whole Ounces that can be mailed for $3.33

$\ge\text{ 11.3 Ounces}$