- The number of students is represented by the variable \(s\).
- The situation is represented by the inequality \(40 - 2s \geq 7\).
- Solving for \(s\), we get \(s \leq 16.5\).
- The maximum number of students is \(\boxed{16}\).
Explanation
- Setting up the Inequality
Let \(s\) represent the number of students in Elisa's math class. Elisa starts with \(40\) lollipops and gives away \(2\) lollipops to each of the \(s\) students. Thus, the total number of lollipops she gives away is \(2s\). The number of lollipops remaining is the starting amount minus the amount given away: \(40 - 2s\). We are told that she has at least \(7\) lollipops remaining, which gives us the following inequality:
\[40 - 2s \geq 7\]
This inequality represents the given situation.
- Solving the Inequality
To find the maximum number of students \(s\), we solve the inequality \(40 - 2s \geq 7\).
First, subtract \(40\) from both sides of the inequality:
\[-2s \geq 7 - 40\]
\[-2s \geq -33\]
Next, divide both sides by \(-2\). Remember that when dividing an inequality by a negative number, the inequality sign must be reversed:
\[s \leq \frac{-33}{-2}\]
\[s \leq 16.5\]
Since \(s\) represents the number of students, it must be a non-negative integer. The largest integer less than or equal to \(16.5\) is \(16\). Therefore, the maximum number of students in Elisa's math class is \(16\).
Examples
Inequalities like this are useful in resource management, such as when you have a fixed budget or supply and need to determine how many items or people you can support. For example, if you have a certain amount of snacks for a party and want to give a fixed portion to every guest while ensuring you keep a reserve for yourself, you can use an inequality to find the maximum number of guests you can accommodate. This helps in planning events or managing inventory efficiently.