Expert: Paul Klarreich - 5/19/2007

Question
Hi, I have one of those damn mix these nuts with those nuts and then you get these nuts, etc. problems that is literally driving me insane. Please help! I know that it is obviously solved by a system of equations, but other than that, I'm at a loss for setting up the equations (I've tried in maybe 10-12 different ways):

A store sells cashews for $5/lb and peanuts for $1.50/lb. The manager decides to be a total dick and mix 30 pounds of peanuts with some cashews and sell the mixture for $3/lb. How many pounds of cashews should be mixed with the peanuts so that the mixture would produce the same revenue as would selling the nuts separately?

Please note that it's not 30 total pounds of nuts. It's 30 pounds of just the PEANUTS!  The total pounds of the nuts mixture (being sold for $3/lb) is 30+C (30 plus the number of cashews mixed in).

Thanks for everything!

Answer
Questioner:   Sam
Category:  Calculus
 
Subject:  Pre-calc
Question:  Hi, I have one of those pesky mix these nuts with those nuts and then you get these nuts, etc. problems that is literally driving me insane. Please help! I know that it is obviously solved by a system of equations, but other than that, I'm at a loss for setting up the equations (I've tried in maybe 10-12 different ways):

A store sells cashews for $5/lb and peanuts for $1.50/lb. The manager decides to be a dishonest person

>> PLEASE! This is a family-oriented site. Since children might read this, I have modified your vocabulary.

and mix 30 pounds of peanuts with some cashews and sell the mixture for $3/lb. How many pounds of cashews should be mixed with the peanuts so that the mixture would produce the same revenue as would selling the nuts separately?

Please note that it's not 30 total pounds of nuts. It's 30 pounds of just the PEANUTS!

>> Okay, okay.  I got it.

The total pounds of the nuts mixture (being sold for $3/lb) is 30+C (30 plus the number of cashews mixed in).

Thanks for everything!

...............................
Hi, Sam,

Looks like your standard mixture problem.  Set up the following table. (And please never call this a chart! That's for history class.)

*********** VIEW IN COURIER FONT **********

Product       Unit Cost  *  Weight   =   Total cost
---------------------------------------------------------
Cashews           5           x             5x
Peanuts           1.5        30             45
---------------------------------------------------------
Mixture           3        x+30             3x + 90

Looks like

5x + 45 = 3x + 90
2x = 45

x = 22.5 pounds of cashews.

Check:

30 pounds of peanuts at 1.50 per gets you  $45
22.5 poinds of cashews at 5 per gets you  $112.50
Those two total  $157.50

52.5 pounds of mixture at 3 per gets you 3 * 52.50 = 157.50

Looks good.