An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the fraction of orange beads Mila uses: 5 3 .
Calculate the number of orange beads Mila uses: 5 3 × 60 = 36 .
Calculate the fraction of orange beads Ben uses: 12 7 .
Calculate the number of orange beads Ben uses: 12 7 × 60 = 35 . Therefore, Mila uses more orange beads: M i l a .
Explanation
Problem Analysis Let's analyze the problem. We know that Mila and Ben both make bracelets with a total of 60 beads. We also know the ratio of red to orange beads for each of them. Our goal is to determine who uses more orange beads.
Calculating Mila's Orange Beads First, let's find out how many orange beads Mila uses. The ratio of red to orange beads for Mila is 2:3. This means that for every 2 red beads, there are 3 orange beads. The total number of parts in this ratio is 2 + 3 = 5 . The fraction of beads that are orange is 5 3 . To find the number of orange beads Mila uses, we multiply this fraction by the total number of beads: 5 3 × 60 = 36 So, Mila uses 36 orange beads.
Calculating Ben's Orange Beads Now, let's find out how many orange beads Ben uses. The ratio of red to orange beads for Ben is 5:7. This means that for every 5 red beads, there are 7 orange beads. The total number of parts in this ratio is 5 + 7 = 12 . The fraction of beads that are orange is 12 7 . To find the number of orange beads Ben uses, we multiply this fraction by the total number of beads: 12 7 × 60 = 35 So, Ben uses 35 orange beads.
Comparison and Conclusion Finally, let's compare the number of orange beads Mila and Ben use. Mila uses 36 orange beads, and Ben uses 35 orange beads. Since 35"> 36 > 35 , Mila uses more orange beads than Ben.
Examples
Understanding ratios and proportions is very useful in everyday life. For example, when baking, you might need to adjust the amount of ingredients based on a certain ratio. If a recipe calls for 2 cups of flour and 1 cup of sugar, and you want to make a larger batch, you can use the ratio 2:1 to calculate the new amounts of flour and sugar needed. This ensures that the taste and texture of the baked goods remain consistent, no matter the size of the batch.
The total charge flowing through the device is 450 coulombs, which is equivalent to approximately 2.81 × 10²¹ electrons. This is calculated using the formula that relates current and charge over time. Therefore, about 2.81 × 10²¹ electrons flow when a current of 15.0 A is delivered for 30 seconds.
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