SOLUTION: A food store makes a 9-lb mixture of peanuts, cashews, and raisins. Peanuts cost $1.50 per pound, cashews cost $2.00 per pound, and raisins cost $1.00 per pound. The mixture calls

Question 196970: A food store makes a 9-lb mixture of peanuts, cashews, and raisins. Peanuts cost $1.50 per pound, cashews cost $2.00 per pound, and raisins cost $1.00 per pound. The mixture calls for twice as much peanuts than cashews. The total cost of the mixture is $13.00. How much of each ingredient did the store use?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
A food store makes a 9-lb mixture of peanuts, cashews, and raisins. Peanuts cost $1.50 per pound, cashews cost $2.00 per pound, and raisins cost $1.00 per pound. The mixture calls for twice as much peanuts than cashews. The total cost of the mixture is $13.00. How much of each ingredient did the store use?


The sentence:

>>...The mixture calls for twice as much 
                       peanuts than cashews...<<


tells us that we are defining peanuts IN TERMS OF cashews.
We like to define things IN TERMS OF x

So let x = the number of lbs. of cashews

And then by that sentence,

the number of lbs. of peanuts = twice x or 2x

Let y = the number of lbs. of raisins. 



Make this chart:

           No. of lbs. | Price per lb. | Price for all lbs.     
Peanuts                |               |       
Cashews                |               |                        
Raisins                |               |           
---------------------------------------------------------
Mixture                |               |             


Put in the expressions for the pounds of each ingredient, and
the total number of pounds of Mixture: 

           No. of lbs. | Price per lb. | Price for all lbs.     
Peanuts        2x      |               |               
Cashews         x      |               |                        
Raisins         y      |               |            
---------------------------------------------------------
Mixture         9      |               |           


Put in the prices per lb. of each ingredient



           No. of lbs. | Price per lb. | Price for all lbs.     
Peanuts        2x      |     1.50      |                 
Cashews         x      |     2.00      |                        
Raisins         y      |     1.00      |           
---------------------------------------------------------
Mixture         9      |               |           


Multiply the no. of pounds by the price per pound to get the
price for all the pounds.  Then put in 13.00 for the price
for all the pounds of mixture: 


           No. of lbs. | Price per lb. | Price for all lbs.     
Peanuts        2x      |     1.50      |     2x(1.50)  
Cashews         x      |     2.00      |      2.00x             
Raisins         y      |     1.00      |      1.00y
---------------------------------------------------------
Mixture         9      |               |     13.00 


Make the first equation from the "no. of lbs." column:

2x + x + y = 9

Make the second equation form the "Price for all lbs." column:

2x(1.50) + 2.00x + 1.00y = 13.00

------

Simplify the first:

2x + x + y = 9
    3x + y = 9

Simplify the second:

2x(1.50) + 2.00x + 1.00y = 13.00
            3x + 2x + 1y = 13
                  5x + y = 13

So we have this system:

 

Solve that and get x = 2, y = 3

So there are x = 2 lbs. of cashews, 
2x = 2(2) = 4 lbs. of peanuts, and
y = 3 lbs. of raisins.

Edwin

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