Mixing Peanuts and CashewsDate: 11/19/1999 at 23:28:15 From: Kelley Remington Subject: Peanuts and Cashews Mixture Problem My daughter has a problem that I have tried to figure out for hours: Peanuts sell for $3.00 per pound. Cashews sell for $6.00 per pound. How many pounds of cashews should be mixed with 12 pounds of peanuts to obtain a mixture that sells for $4.20 per pound? I sure hope you answer my question or I will never be forgiven for not knowing how to solve this problem. I will go out and buy a book if you are unable to answer my question. Thank you, Kelley Remington Date: 11/20/1999 at 10:54:08 From: Doctor Anthony Subject: Re: Peanuts and Cashews Mixture Problem Let C be the weight of cashews to buy. Total cost of mixture = (12 x 3) + (C x 6) = (12+C) x 4.2 36 + 6C = 50.4 + 4.2C 1.8C = 14.4 C = 8 So you need to buy 8 pounds of cashews. - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ Date: 06/23/2000 at 17:02:57 From: Doctor Johnny Subject: Re: Peanuts and Cashews Mixture Problem Kelly, Hello there. My name is Dr. Johnny. I am a high school algebra teacher who really understands your frustrations. When trying to teach this same type of problem to high school students, I find that they experience a variety of concerns. I hope I can help you to better understand this situation. The best way to set up this problem is to construct a table that shows the relations among the 3 items (peanuts, cashews, and mixture). Type Cost per pound Pounds Total Cost ---- -------------- ------ ---------- Peanuts $3.00 12 3(12) = 36 Cashews $6.00 x 6x Mixture $4.20 12+x 4.20(12+x) Here are some explanations for why I set the chart up this way. The peanuts line is pretty self-explanatory. The amount for the cashews is the unknown, because you know the least about that part of the problem. The mixture is made up of cashews and peanuts, so the amount of the mixture is the same as the amount of peanuts + the amount of cashews. From here, we know that the cost of the peanuts and cashews must be the same as the mixture: 36 + 6x = 4.20(12+x). Now we must simplify the equation to obtain the amount of cashews needed to satisfy the problem. 36 + 6x = 4.2(12+x) 36 + 6x = 50.4 + 4.2x Distributive property 6x - 4.2x = 50.4 - 36 Get the variables on one side and the constants on the other 1.8x = 14.4 Combine like terms x = 8 Division property of equality We now have a value that we anticipate is the answer. Let's check to see if it makes sense: 12 pounds of peanuts @ $3.00 per pound costs $36 8 pounds of cashews @ $6.00 per pound costs $48 20 pounds of mixture @ $4.20 per pound costs $84 $36 + $48 does equal $84; therefore 8 pounds of cashews does make this situation hold true. I always tell my students to look at the smaller pieces of the picture instead of trying to look at the whole picture, because all of that information can run together and really get a person confused. Good luck in the future and if you ever need any additional help, feel free to write. - Doctor Johnny, The Math Forum http://mathforum.org/dr.math/ Date: 11/20/1999 at 19:44:33 From: Kelley Remington Subject: Re: Peanuts and Cashews Mixture Problem Thank you for your answer. I finally figured it out but went about it a different way. Thank you so much for your answer though. |
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