- The total number of bird species is \(68\), consisting of \(24\) species that stayed and \(b\) species that were transported.
- The total is the sum of the two groups, leading to the relationship: \(68 = 24 + b\).
- Using the commutative property of addition, we can rewrite the equation as \(b + 24 = 68\).
- The correct choice is \(\boxed{b + 24 = 68}\).
Explanation
- Analysis of the problem data
The problem states that the Roaring Zoo houses a total of \(68\) bird species. Out of these, \(24\) species stayed at the zoo, and the remaining number of species, denoted by \(b\), were transported to the barn to escape the cold weather. To find the correct equation for the number of transported birds, we need to express the total number of species as the sum of those that stayed and those that were moved.
- Setting up the equation
The relationship between the categories can be expressed as:
\[\text{Total species} = (\text{Species that stayed}) + (\text{Species transported})\]
Substituting the given values into this relationship, we have:
\[68 = 24 + b\]
By the commutative property of addition, the order in which we add the terms does not change the result, so this is equivalent to:
\[b + 24 = 68\]
This equation correctly represents that the sum of the transported species (\(b\)) and the species that stayed (\(24\)) equals the total number of bird species (\(68\)).
- Selecting the correct equation
Comparing our derived equation \(b + 24 = 68\) with the given options:
- \(b + 68 = 24\) (Incorrect)
- \(b - 68 = 24\) (Incorrect)
- \(b + 24 = 68\) (Correct)
- \(b - 24 = 68\) (Incorrect)
Thus, the correct equation that represents the number of species transported is \(b + 24 = 68\).
Examples
Understanding how to model relationships with equations is fundamental in management and logistics. For example, if you manage a warehouse with a total inventory of items and some are shipped out, you use a similar equation to track remaining stock: \(\text{Initial Inventory} = \text{Remaining Items} + \text{Shipped Items}\). Learning to structure these problems algebraically helps you organize data and make accurate predictions in everyday tasks, from inventory tracking to budget planning.