mixture problem

The manager of a specialty food store combined almonds that cost $4.50 per pound with walnuts that cost $2.50 per pound. How many pounds of each were used to make a 100-pound mixture that cost $3.24 per pound.

Relationship: The sum of the value of the ingredients is equal to the sum of the value of the mixture.

I have two ideas on how to solve this problem:

4.50x + 2.50x =100(3.24)
7.50x= 324
x=43.2

the other is:

4.50x + (1-x)2.50= 324
4.50x + 2.50-2.50x=324
2x=321.5
x= 160.75

You need more ideas.

Other Relationship: The sum of the weights of the two ingredients must be 100 lbs.

Here is an idea you are missing: WRITE DOWN your definitions. You will never make the error you made if you WRITE DOWN your clear and concise definitions.

You started using 'x' with no warning and then you became confused as to what it means. Try it this way...

A = Pounds of Almonds required for the mixture

Once you have done this, you will not EVER be tempted to to use 'A' to be the number of pounds of Walnuts. See how that might be helpful?

Since A is the pounds of Amonds and 100 is the total poundage, the pounds of Walnuts must be 100-A!!

NOW find your relationship.

4.50*A + 2.50*(100-A) = 3.24*100