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Have you ever wondered how to determine the cost of tomatoes per kilogram from a given total price? Let's dive into this intriguing question together.
Imagine you are a farmer who recently sold 26 kilograms of tomatoes for a total of $78. How would you calculate the cost per kilogram? Pause for a moment and think about it before we proceed. The answer lies in understanding the concept of slope, a fundamental mathematical principle that helps us analyze the relationship between two variables.
Slope, often represented as the change in y over the change in x, is a measure of how much one variable changes in relation to another. In this scenario, y represents the cost in dollars, while x represents the weight in kilograms. By dividing the total cost by the total weight, we can find the unit price.
But what exactly does this mean? Let's break it down. We have $78 for every 26 kilograms of tomatoes. To find the cost per kilogram, we need to divide $78 by 26. A simple calculation reveals that 78 is exactly three times 26, which means the cost per kilogram is $3.
Now, how does this relate to the concept of slope? The slope of three indicates that for every additional kilogram of tomatoes, the cost increases by $3. This is a crucial insight that can help us analyze different scenarios and make informed decisions.
But hold on, there's more! Let's say we have several graphs representing different slopes. How can we determine which graph accurately represents the cost of tomatoes per kilogram? Here's where the slope comes into play. We need to find a graph where the slope is three, meaning that every time the weight increases by one kilogram, the cost increases by $3.
Upon examining the graphs, we can quickly rule out some options. In one graph, when the weight increases by one kilogram, the cost increases by only $1, which doesn't match our calculation. In another, the cost seems to increase by only 1/3 for each additional kilogram, which is also incorrect. However, there is one graph where the cost increases by $3 whenever the weight increases by one kilogram. This is the correct representation of our scenario.
So, there you have it! By understanding slope and applying it to our problem, we've successfully decoded the cost of tomatoes per kilogram. This knowledge not only enhances our mathematical skills but also provides valuable insights into pricing and economic decision-making.
In conclusion, the true cost of tomatoes per kilogram is $3, as indicated by the slope of three. By unraveling this mystery, we've gained a deeper understanding of the relationship between cost and weight, empowering us to make more informed choices in the future.
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