Oskar and Lakshmi are baking cookies for a bake sale. Both are using the same re
ID: 3034188 • Letter: O
Question
Oskar and Lakshmi are baking cookies for a bake sale. Both are using the same recipe; but Lakshmi has a larger oven, so she is making a larger batch of cookies than Oskar is. Oskar is using a cups of flour, while Lakshmi is using b cups of flour. Answer the following questions, and use algebraic structure to justify your answers.
How many times as large as Oskar’s batch of cookies is Lakshmi’s batch? If Oskar is using m cups of sugar, how many cups of sugar is Lakshmi using? If Lakshmi is using k cups of butter, how many cups of butter is Oskar using? If Oskar and Lakshmi sell all of the cookies they make at the same price and earn a total of R dollars, then how much money did Oskar’s cookies earn?
Explanation / Answer
Q. How many times as large as Oskar's batch of cookies is Lakshmis batch?
A. Lakshmi's oven is bigger, so in a batch, she would make more cookies at a time, using more flour. Hence number of 'b' cups of flour used by her would be more than 'a' cups of flour used by Oskar. Lakshmi would be using (b-a) cups of flour more for a batch of cookies. This would be (b-a)/a times more than Oskar. Accordingly, Lakshmi's batch of cookies would be (b-a)/a times as large as Oskar's batch of cookies.
Q. If Oskar is using m cups of sugar, how many cups of sugar is Lakshmi using?
A. If Oskar is using m cups of sugar for one batch of cookies, then sugar required per cup of flour is 'm/a' cups. Since Lakshmi is using 'b' cups of flour, she would use 'b(m/a)' cups of sugar.
Q. If Lakshmi is using 'k' cups of butter, how many cups of butter is Oska using?
A. If Lakshmi is using 'k' cups of butter for a batch of cookies, then butter required per cup of flour is 'k/b' cups. Since Oskar is using 'a' cups of flour for a batch, butter required by him would be 'a(k/b)' cups
Q If Oskar and Lakshmi sell all the cookies they make at the same price and earn a total of R dollars, then how much money did Oskar cookies earn?
A. Suppose Oskar makes 'n' number of cookies in batch using 'a' cups of flour, then output of cookies per cup of flour would be 'n/a' number of cookies.Thus Lakshmi would be making 'b(n/a)' number of cookies in 'b' cups of floor. The total number of cookies made by Oskar and Lakshmi would be ' n + b(n/a)' or ''n(a+b)/a ' . If 'p' dollars is the selling price per cookie, then the total number of cookies would sell for p* n(a+b)/a = R dollars. Now solving for p, this equation would give p=Ra/n(a+b) dollars. Thus Oskar would make n*p dollars, or Ra/(a+b) dollars
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