An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Find the amount of sugar per cookie: 24 1 2 1 = 16 1 .
Multiply the sugar per cookie by the desired number of cookies: 16 1 × 36 = 16 36 .
Simplify the fraction: 16 36 = 4 9 .
Convert to a mixed number: 4 9 = 2 4 1 . The final answer is 2 4 1 cups.
Explanation
Problem Analysis Let's analyze the problem. We know that 24 cookies require 1 2 1 cups of sugar. Ben wants to make 36 cookies, and we need to find out how much sugar he needs.
Sugar per Cookie First, we need to find out how much sugar is needed for each cookie. We can do this by dividing the total amount of sugar by the number of cookies the recipe makes. So, we have: s ug a r P er C oo ki e = 24 1 2 1 We can convert the mixed number to an improper fraction: 1 2 1 = 2 3 So, s ug a r P er C oo ki e = 24 2 3 = 2 3 ÷ 24 = 2 3 × 24 1 = 48 3 = 16 1 So, each cookie requires 16 1 cups of sugar.
Sugar for 36 Cookies Now that we know how much sugar each cookie needs, we can find out how much sugar Ben needs for 36 cookies. We multiply the amount of sugar per cookie by the number of cookies Ben wants to make: s ug a r F or 36 C oo ki es = 16 1 × 36 = 16 36 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4: s ug a r F or 36 C oo ki es = 16 ÷ 4 36 ÷ 4 = 4 9 Now, we convert the improper fraction 4 9 to a mixed number: 4 9 = 2 4 1 So, Ben needs 2 4 1 cups of sugar to make 36 cookies.
Final Answer Therefore, Ben needs 2 4 1 cups of sugar to make 36 cookies.
Examples
Understanding ratios and proportions is crucial in everyday life, especially when adjusting recipes. For instance, if you're baking and need to scale a recipe up or down, knowing how to adjust ingredient quantities ensures the final product turns out as expected. Similarly, in cooking, if you want to double a recipe, you need to double all the ingredients. This concept also applies to mixing cleaning solutions, calculating fuel mixtures for engines, or even adjusting paint quantities for a project, ensuring accuracy and consistency in various tasks.
