Cake Recipe Ratio
Date: 03/05/2003 at 21:36:28 From: Lavos Subject: This is a math problem I really need help with... Cake Recipe A recipe for four-egg cake calls for the ingredients listed below and is supposed to be baked in three 9-inch-diameter round cake pans. Unfortunately, you have three 10-inch-diameter cake pans. You want to make your cake about the same height as it would have been in a 9-inch-diameter cake pan. Determine the amounts needed for each ingredient. (Hint: do the eggs first.) Ingredients: 2 2/3 cups of cake flour 2 1/4 teaspoons of baking powder 1 cup butter 2 cups sugar 4 eggs 1 cup of milk One of the methods I tried was to find the volume of both cake pans (the 9-inch and the 10-inch) and divide the smaller one by the bigger one. This gave me approximately 0.81 or 81%. I then subtracted 1 by the 81% and got 0.19. I multiplied 4 (because there are four eggs) by 0.19 and got 0.79 and then added that to the original four. The answer was 4.79, making the total eggs needed 4.79. I don't know if this is the solution though. It's a hard problem and I was hoping you could help me.
Date: 03/05/2003 at 23:04:06 From: Doctor Peterson Subject: Re: This is a math problem I really need help with... Hi, Lavos. You used some good ideas, but I'm not sure you put them together right. I would approach it a little differently, so as to be sure of getting the right ratios. You found that the ratio of base areas, and therefore of volumes at the same depth, is 81:100. That's a great start. Now, that means that you want to multiply every ingredient by 100/81. Do you see that? They tell you to start with the eggs; you will need 100/81 * 4 = almost 5 eggs. Since recipes are generally a little flexible, I would just go with 5 eggs and keep multiplying everything by 100/81 (so that there will be just a slight increase in the proportion of egg - after all, eggs vary in size anyway). They might expect you instead to adjust your ratio from 100/81 to 5/4 so that everything agrees with the number of eggs (and then check that your pan won't be too full); but I don't think that is necessary in practice. In my mind, I'm just making sure that I don't have to round too far in doing this; if it had turned out to need 4.5 eggs, I might have wanted to check how sensitive the recipe is to the number of eggs before going ahead with the rounding. Your method was essentially multiplying everything by (1 - 81/100)+1, which is equal to 1.19, rather than by 100/81 = 1.23. You would be close, but the method is not correct. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 03/05/2003 at 23:27:28 From: Lavos Subject: Thank you (This is a math problem I really need help with...) You helped me a lot with this problem and got back to me very fast. I see where my mistake was and I fixed it. Now that I see how to do it I can fix my problem. Thank you VERY much for all the help. -Lavos
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