Question

Jessie will pack a suitcase with books. Total weight of the suitcase and books can be no more than 50 pounds. The empty suitcase weighs 5.7 pounds . Each book weighs 2.4 what is the greatest number of books that jessie can pack in the suitcase?please explain why

Answer 1

If the empty suitcase weighs 5.7 pounds and each book weighs 2.4 pounds, the total weight can be written as:

`W=5.7+2.4n`

where n is the number of books.

If the total weight has to be less or equal than 50, we can write:

`\begin{gathered} W\le50 \\ 5.7+2.4n\le50 \\ 2.4n\le50-5.7 \\ 2.4n\le44.3 \\ n\le(44.3)/(2.4) \\ n\le18.45 \end{gathered}`

As n<=18.45, we know that Jessie can take up to 18 books, as the number of books is an integer.

We can check if the total weight is under 50 as:

`\begin{gathered} W=5.7+2.4\cdot18 \\ W=5.7+43.2 \\ W=48.9 \end{gathered}`

The inequality is satisfied, and if we add one more book the weight goes to 48.9+2.4=51.3, which is over the limit.

Answer: 18 books.