SOLUTION: A coffee store will start selling a mix of two kinds of coffee: Kona and Mexican Organic. The price of Kona coffee is $7.50 per pound and the price 
 of Mexican Or
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Question 280583: A coffee store will start selling a mix of two kinds of coffee: Kona and Mexican Organic. The price of Kona coffee is $7.50 per pound and the price
of Mexican Organic coffee is $8.30 if they are sold separately. The store wants the price of the mix to be $8.00 per pound.
How many pounds of each kind should be used to prepare 160 pounds of the mix?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Price of Kona = $7.50/lb
Price of Mexican Organic = $8.30/lb
x = weight of Kona coffed in the mix
7.5x = value of the given weight of Kona coffee
y = weight of Mexican Organic coffee in the mix,
8.3y = value of the given weight of Mexican Organic coffee
.
We are asked to end up with 160 lb @ $8 /lb = a value of $1280.
7.5x + 8.3y = 1280
.
We note that x+y = 160
so it's easier to say x = 160-y or y = 160-x to define the two weights using only one variable, 'x'.
.
7.5x + 8.3(160-x) = 1280
multiply by 10 to eliminate the decimal
75x + 83(160-x) = 12,800
75x + 13,280 - 83x = 12,800
collect 'x'
-8x + 13,280 = 12,800
subtract 13,280 from both sides
-8x = -480
divide both sides by -8
x = -480/-8 = 480/8 = 60
.
substitute
x + y = 160
60 + y = 160
subtract 60 from both sides
y = 100
.
check the values to see if we're right
specifically, does 7.5x + 8.3y = 1280?
7.5x = 7.5*60 = 450
8.3y = 8.3*100 = 830
450 + 830 = 1280
.
Answer:
To make 160 lbs of a coffee blend using the Kona and Mexican Organic coffee that would be fairly priced at $8/lb, you would add 60 lb of Kona @ $7.50/lb and 100 lb of Mexican Organic @ $8.30/lb.
.
Done.
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