- To solve for \(y\) in the equation \(13.25y = 79.5\), divide both sides by \(13.25\).
- Calculate the quotient: \(y = \frac{79.5}{13.25} = 6.00\).
- The correct choice is \(6.00\).
- Final answer: \(\boxed{6.00}\).
Explanation
- Problem Analysis
We are given the linear equation \(13.25y = 79.5\). The goal is to isolate the variable \(y\) to find its value. In this equation, \(y\) is multiplied by the coefficient \(13.25\). To find \(y\), we need to reverse this multiplication by dividing both sides of the equation by \(13.25\).
- Solving for \(y\)
To solve for \(y\), we perform the division:
\[y = \frac{79.5}{13.25}\]
By calculating the value of this quotient, we find:
\[y = 6.00\]
This value corresponds to the first option provided in the problem description.
Examples
Understanding how to isolate a variable is a fundamental skill in algebra. For example, if you are planning a trip and need to calculate how many hours (\(y\)) it will take to travel a certain distance at a fixed speed, you might have an equation like \(Speed \times Time = Distance\). If you know your average speed is \(13.25 \text{ km/h}\) and the total distance is \(79.5 \text{ km}\), solving \(13.25y = 79.5\) tells you exactly how many hours the journey will take, helping you manage your schedule effectively.