Question

Moving The van that you are using to move can hold 16 moving boxes. Each box can hold 60 pounds of books or 15 pounds of clothes. Let \(b\) represent the number of boxes filled with books. Write a function that represents the total weight \(w\) of the boxes in the van.

Short answer

The function that represents the total weight \(w\) of the boxes in the van is \(w(b) = 45b + 240\)

Step-by-step solution

Understand the Problem

The van can carry 16 moving boxes and each box is either filled with books or clothes. For boxes filled with books, each box can hold 60 pounds. Let's represent boxes filled with books by letter \(b\). Given these, the weight contribution by the book boxes is \(60b\). Total boxes are 16, so, boxes filled with clothes would be \(16-b\), because total boxes are either filled with books or clothes. Each clothes box can carry 15 pounds, so these boxes contribute \(15(16-b)\) towards the total weight.

Formulate the Equation

The total weight in the van will be the weight of the boxes filled with books plus the weight of the boxes filled with clothes. Working with the details discussed, we formulate our function to be \(w(b) = 60b + 15(16 - b)\). This is how the total weight of the boxes is distributed into weight from book boxes and clothes boxes.

Simplify the Function

To further simplify the function \(w(b)\), distribute the 15 in the second term: \(w(b) = 60b + 240 - 15b\). And then combine like terms to get the final function \(w(b) = 45b + 240\)