Juice for Fifty
(page 164)
 Oh boy! A controversy! Here we have two student-created solutions that disagree... Jessica and Dani are located in Cincinnati, Ohio at Pleasant Run Middle School. They are 6th graders in Ms. Lowe's math class: This is a group from Ms. Airing's class at West Middle School in Westminster, Maryland: Question: How many half-gallon pitchers do you need? We first wrote down all the information needed to solve this problem. Then we figured that one half-gallon pitcher is 64 fluid ounces or 8 cups, which supplies 8 people, one cup per person. So seven half gallon pitchers are 56 cups, suppling 56 people meaning we would have 6 cups left over because we are only suppling 50 people. ANSWER: We need 7 half-gallon pitchers. Question: How many cans of frozen orange juice do you need? We first wrote down all the information needed to solve this problem. Then we figured that 50 cups times 8 ounces for each cup equals 400 ounces, but each can of frozen orange juice is 12 ounces. So we then divided 400 ounces by 12 to see how many cans of frozen orange juice we needed, which equals 34 cans. ANSWER: We need 34 cans of frozen orange juice. Question: How many cans of water do you need? We first wrote down all the information needed to solve this problem. Then we figured that since there is three cans of water in each one can of frozen orange juice and we needed 34 cans of frozen orange juice, that all we have to do is multiply 34 by 3 because we need 3 cans of water for each can of frozen orange juice, which equals 102 cans. ANSWER: We need 102 cans of water. Question: How much will it cost? We first wrote down all the information needed to solve this problem. Then we figured that it costs \$1.19 per can of frozen orange juice. So all we needed to do was multiply the 34 cans of frozen orange juice that we needed by \$1.19 for each can to get how much it costs, which equals \$40.46. ANSWER: It will cost us \$40.46 for 38 cans of frozen orange juice. Question: If you got a deal for \$0.89 per can of frozen orange juice, how much would it cost? We first wrote down all the information needed to solve this problem. Then we figured that since it was only \$0.89 per can of frozen orange juice and we needed 34 cans of frozen orange juice, all we needed to do was multiply the 34 cans of frozen orange juice by \$0.89 per can to find out how much it costs, which equals \$30.26. ANSWER: If we got a deal for \$0.89 per can of frozen orange juice it would cost us \$30.26. I would first like to say that our class did your "Juice For Fifty" problem and the class found that the solution to the problem [the one posted on the web] is incorrect. This is how my group, Jen (me), Jen, Brittany, and Elizabeth (Liz) found the correct solution to your problem. We each got one question. Our group worked together as a team to figure out 4 different questions. In the end, we found our answers and this is how we got them: First, we found out how many cans of orange juice we would need. We did this by multiplying the amount of people, which was 50, by the amount of ounces each person would drink, which is 8 ounces. The answer we found was 400 ounces. We then had to divide the amount of ounces in each can of frozen orange juice, which was 48 ounces. Our answer was 8.3 reapeating which we had to round up to 9 so we had enough cans.  Now, finished answering question #1, we moved to the next one. Which was to find how many cans of water we need to make orange juice along with 9 cans of frozen orange juice. Taking information from one of our clues, we know that we need three cans of water per can of frozen orange juice. All we needed to do was to multiply the amount of canned frozen oranje juice, 9, by the amount of can of water per can of frozen orange juice. Our answer is 27 cans of water needed, thus answering our second question. Our third question was quite simple to answer. The question asked how much it would cost to make enough orange juice for 50 people. One of our clues stated that one can of frozen orange juice was \$1.19. With this all we had to do was multiply \$1.19 by the amount of frozen orange juice. Our total price, we found, was \$10.71. Finally, we were on our last question. The question was to find out how many pitchers you would need to make orange juice for 50 people. We multiplied the amount of people by the amount of how many ounces  each person would drink. The answer was 400 ounces. Then all we needed to do was divide that number by the amount of ounces each pitcher contained. The final answer was 7 pitchers. Thus, this is how we found the answers to all of the questions on "Juice For Fifty". Thank you for your time in reading this letter and please consider posting this response on your webpage. Please email me back as soon as possible! Thank you again and good night. eeps comments: Wow! It took a alot of writing, but THIS is a great example of showing your thinking. Now, readers, how are the solutions different? Which is right? If someone made a mistake, what was it? Is it possible that they are both right? With this much to go on (and this question is unusual in that it has many questions to answer, so most of the time you don't have to write this much, honest) if there's a problem, you can tell where it is. Now, here is a response from Lane, Danny, and Kelly of West Middle School. Is it any different from the ones above? My group believes that we have figured out your Juice for 50 math problem. The first thing we figured out was how many cans of orange juice we would need for a total of 50 people. We figured out that we needed 8.3(9) cans of orange juice by multiplying 50 (amount of people we had) by 8 (fluid ounces in the can) and we got 400. Then we divided 400 by 48 and got 8.3(repeating) so we rounded up to get 9 (to make sure we had enough). The second thing we found out how to do was how much money we would need to spend to buy all the orange juice. If each can cost \$1.19 and we needed 9 cans then that would be \$10.71. The third thing we found out how to do in this problem was how many cans of water we needed. If for every can of orange juice we needed 3 cans of water, then all we had to do was multiply 9 (cans of OJ) by 3. We then got 27. We would need 27 cans of water. The very last thing we found out how to do in Juice for 50 was hoy many pitchers we would need. We had 9 cans of OJ and multiplied that by 12 (for can) ad got 408. Then we divided 408 by 64 (per pitcher) and got 6.75 which we rounded up to get 7 (so we once again would know we had enough). We would need 7 half-gallon pitchers. **My group believes the answers on the website are incorrect because of the 12 ounces of orange goo that was left over in the can. We do not think that was taken into consideration with your answers because we made the same mistake ourselves and caught it.** Thank you, Lane, Danny, and Kelly, West Middle School One last idea: this problem was written way back in the days when water was usually free. Nowadays a lot of people use bottled water. Suppose you were so into bottled water that you used it to make orange juice. How much more would it cost to make juice for fifty? How does that compare with buying orange juice in cartons? Find prices at your store and see what you get. back to the Answer Book page