Question

Christina is packing different books into boxes. The paperback booksweigh 0.8 pounds each. The hardcover books weigh 1.3 pounds each.Christina needs to pack the boxes so there are at least 20 books in each box, but the boxes cannot weigh more than 30 pounds. If x represents thenumber of paperback books, and y represents the number of hardcoverbooks, identify Christina's set of constraints (Check all that apply).

Answer 1

Step 1. Identify the variables.

`\begin{gathered} x\longrightarrow\text{ Number of }paperback\text{ books} \\ y\longrightarrow\text{Number of }hardcover\text{ books} \end{gathered}`

Step 2. Find the first constraint using the condition for the total number of books in each box.

The problem states "Christina needs to pack the boxes so there are at least 20 books in each box" This means that the sum of x and y must be at least 20, this is represented in the following inequality:

`x+y\ge20`

That is the first constraint.

Step 3. Find the second constraint using the condition for the weight of each box.

The problem states: "the boxes cannot weigh more than 30 pounds" and since the paperback books weigh 0.8 pounds and the hardcover books weigh 1.3 pounds each, the sum of their weights is:

`0.8x+1.3y`

This sum cannot be more than 30, which is represented by the following inequality:

`0.8x+1.3y\leq30`

Answer:

The set of constraints is

`\begin{gathered} x+y\ge20 \\ 0.8x+1.3y\leq30 \end{gathered}`