Select the correct answer from each drop-down menu. Gino is buying wood screws at the corner hardware store. The table shows different numbers of bags of screws and their corresponding prices. According to the table, the relationship between the number of bags and the price is $\square$
Answer (2)
The relationship between the number of bags of screws and their price is proportional, as the price per bag remains constant at $5. By calculating the price for different amounts of bags, we see that the ratio does not change, confirming proportionality. Thus, you would fill in the square with the word 'proportional.'
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Calculate the price per bag for each row: 2 10 = 5 , 4 20 = 5 , 7 35 = 5 .
Compare the price per bag for each row.
Since the price per bag is the same for all rows, the relationship is proportional.
The relationship between the number of bags and the price is p ro p or t i o na l .
Explanation
Understanding the Problem We are given a table that shows the relationship between the number of bags of screws and their prices. We need to determine if the relationship between the number of bags and the price is proportional.
Checking for Proportionality To determine if the relationship is proportional, we need to check if the ratio of the price to the number of bags is constant. In other words, we need to calculate the price per bag for each row in the table and see if they are the same.
Calculating Price per Bag (Row 1) For the first row, the price per bag is 2 10 = 5 dollars.
Calculating Price per Bag (Row 2) For the second row, the price per bag is 4 20 = 5 dollars.
Calculating Price per Bag (Row 3) For the third row, the price per bag is 7 35 = 5 dollars.
Conclusion Since the price per bag is the same for all rows (5 dollars per bag), the relationship between the number of bags and the price is proportional.
Examples
Understanding proportional relationships is crucial in everyday life. For instance, when buying groceries, the price of an item is often proportional to its weight. If 1 kg of apples costs $2, then 2 kg of apples will cost $4. This concept helps us estimate costs and make informed purchasing decisions. Similarly, in cooking, recipes often maintain proportional relationships between ingredients. If a recipe calls for 2 cups of flour and 1 cup of sugar, doubling the recipe would require 4 cups of flour and 2 cups of sugar to maintain the same taste and consistency.
