SOLUTION: How many pounds of cashews that cost $14 per pound must be mixed with 5 pounds of peanuts that cost $6.50 per pound to make mixed nuts that cost $10.25 per pound? I can't seem t

Algebra ->  Expressions-with-variables -> SOLUTION: How many pounds of cashews that cost $14 per pound must be mixed with 5 pounds of peanuts that cost $6.50 per pound to make mixed nuts that cost $10.25 per pound? I can't seem t      Log On


   



Question 1094014: How many pounds of cashews that cost $14 per pound must be mixed with 5 pounds of peanuts that cost $6.50 per pound to make mixed nuts that cost $10.25 per pound?
I can't seem to put this into an equation...

Found 4 solutions by Alan3354, richwmiller, ikleyn, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
$10.25 is the average.
Equal amounts.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
14c+5*6.50=(5+c)*10.25
14c+32.50=51.25+10.25c
14c-10.25c=51.25-32.50
3.75c=18.75
c=18.75/3.75
c=5
Like the man said equal amounts
14+6.50=20.50
10.25 is half of 20.50

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
See the lessons
    - Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts
    - Word problems on mixtures for dry substances like candies, dried fruits
in this site for this kind of problems.


Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Mixture problems".

Read them and become an expert in solution the mixture word problems.


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!

Always think about how you can find the answer to a problem with as little effort as possible.

The third response you got to this question suggests that you should always use the formal algebraic methods in the references she shows to solve problems like this.

The second response shows a standard algebraic solution, confirming the answer given in the first response.

The first response looks at the cost per pound of the cashews, the mixed nuts, and the final mixture, and sees that the cost per pound of the final mixture is exactly halfway between the costs of the two ingredients; and it immediately concludes from that that the amounts of the two ingredients must be equal.

Which method got to the answer with the least amount of work?

Always spend some time thinking about a problem before you start actually trying to solve it, to see if there is an easy path to the solution.