Associated Topics || Dr. Math Home || Search Dr. Math

### Mixing Peanuts and Cashews

```
Date: 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

```
Associated Topics:
Middle School Algebra
Middle School Word Problems

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search