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Question 202057: 1. A store mixes Barzilian coffee worth $12 per kilogram and Turkish coffee worth $16 per kilogram. The mixture is to sell for $13 per kilogram. Find how much of each should be used to make a 120-kilogram mixture.
Kilograms of Brazilian coffee= ?
Kilograms of Turkish coffee= ?
2.Soybean meal is 16% protein; cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 11% protein?
Lbs of Cornmeal in the mixture= ?
Lbs of Soybean meal in the mixture= ?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! 1. Let x = the number of kilograms of Brazilian coffee at $12 per kilogram, then (120-x) = the number of kilograms of Turkish coffee at $16 per kilogram. Together, these two amounts add up to 120 kilograms of the mixture at $13 per kilogram.
You have enough information to write the necessary equation to solve for x.
$12(x)+$16(120-x) = $13(120) Simplify.
12x+1920-16x = 1560 Combine the x-terms on the left side.
-4x+1920 = 1560 Now subtract 1920 from both sides.
-4x = -360 Finally, divide both sides by -4.
x = 90 and...
120-x = 120-90 = 30.
The store will need to mix 90 kilograms of Brazilian coffee with 30 kilograms of Turkish coffee to obtain 120 kilograms of the mixture.
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2. Let x = the number of lbs. of Soybean meal at 16% protein, then (320-x) = the number of lbs. of Cornmeal at 8% protein. The sum of these two amounts are to add up to 320 lbs. of mixture at 11% protein. After changing the percentages to their decimal equivalents, you can write the equation required to solve for x.
0.16x+0.08(320-x) = 0.11(320) Simplify.
0.16x+25.6-0.08x = 35.2 Combine the x-terms on the left.
0.08x+25.6 = 35.2 Subtract 25.6 from both sides.
0.08x = 9.6 Finally, divide both sides by 0.08
x = 120 and...
320-x = 320-120 = 200, so...
You will need to mix 120 lbs. of Soybean meal with 200 lbs of Cornmeal to obtain 320 lbs. of the mixture.
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