Look at another example.
Jessica and Jaime eat out at a restaurant. The bill comes to n dollars, and they leave a 22% tip for their server. There are two ways Jessica and Jaime can write an expression to represent their total cost.
The first way is to write the base cost and the tip as two separate parts. In this example, the base cost is n . The tip is 22% of n . Because 22% is equal to 0.22, the amount of the tip can be written as 0.22n . To find the total, write an expression that adds these two separate amounts: In all, Jessica and Jaime spend n + 0.22n dollars.
Before you read ahead, think of what you know about mathematical structure. Is there a way to combine these two terms according to the rules of mathematical operations?
The second way is to combine the two terms above into a single term.
Because n = 1n , n + 0.22n can be thought of as 1.22n .
Which expression is correct? Again, the answer is both. The first way has the advantage of breaking down the amounts to make it clearer how much money Jessica and Jaime are spending on the meal compared to how much they are spending on the tip.
The second focuses more specifically on the total cost without looking at the breakdown. Looking at the problem from both perspectives helps you see the relationship between them and deepens your understanding of what the problem is all about.
Both expressions are correct. They represent the same value and can be used interchangeably. The first expression breaks down the base cost and tip separately, while the second expression combines them into a single term. Both expressions provide different perspectives on the problem and contribute to a deeper understanding of the relationship between the base cost and the tip.
Both expressions are correct.
The first expression, "n + 0.22n," represents the total cost by adding the base cost (n) and the tip amount (0.22n) separately. This allows for a clear breakdown of the amounts spent on the meal and the tip.
The second expression, "1.22n," combines the base cost and the tip amount into a single term. This represents the total cost without explicitly separating the amounts spent on the meal and the tip.
Both expressions convey the same information and provide different perspectives on the total cost.
Yes, both expressions are correct and represent the total cost of Jessica and Jaime's meal. The first expression, n + 0.22n, breaks down the total cost into the base cost (n) and the tip (0.22n). This can help to visualize and understand how much they are spending on the meal compared to the tip.
The second expression, 1.22n, combines the base cost and the tip into a single term. This gives the total cost directly without explicitly stating the breakdown. This expression focuses solely on the total cost without considering the individual components.
Both expressions are mathematically equivalent and represent the same total cost. Choosing between them depends on the context and purpose of the problem. The first expression provides a clearer breakdown of the costs, while the second expression emphasizes the total cost.
Analyzing the problem from both perspectives can deepen your understanding and help you see the relationship between the two expressions.