Ex1)You need a 40% alcohol solution. On hand, you have a 280 mL of a 20% alcohol mixture. You also have 75% alcohol mixture. How much of the 75% mixture will you need to add to obtain the desired solution?
Ex2)A coffee distributor needs to mix a(n) Rift Valley coffee blend that normally sells for $8.40 per pound with a House coffee blend that normally sells for $14.70 per pound to create 40 pounds of a coffee that can sell for $11.08 per pound. How many pounds of each kind of coffee should they mix?
Ex2)A coffee distributor needs to mix a(n) Rift Valley coffee blend that normally sells for $8.40 per pound with a House coffee blend that normally sells for $14.70 per pound to create 40 pounds of a coffee that can sell for $11.08 per pound. How many pounds of each kind of coffee should they mix?
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1) Use the following relationship for each solution:
Volume * concentration = pure alcohol
Let x be the volume of the 75% alcohol solution.
pure alcohol (in X ml of 75%) = 0.75x
The pure alcohol in 280mL of the 20% alcohol solution is
pure alcohol = 280(0.20)
The pure alcohol in the final mixture of x+280 mL of 40% alcohol is
pure alcohol = (280 + x)(0.40)
Thus
0.75x + 280(0.20) = (280 + x)(0.40)
Solving for x,
x = 160 mL of 75% alcohol mixture used
2) Let R be the amount of the Rift Valley coffee and H be that of the House coffee.
8.40R + 14.70H = 40(11.08)
R + H = 40
Solving these 2 equation simultanneously,
R = 22.984
H = 17.016
Volume * concentration = pure alcohol
Let x be the volume of the 75% alcohol solution.
pure alcohol (in X ml of 75%) = 0.75x
The pure alcohol in 280mL of the 20% alcohol solution is
pure alcohol = 280(0.20)
The pure alcohol in the final mixture of x+280 mL of 40% alcohol is
pure alcohol = (280 + x)(0.40)
Thus
0.75x + 280(0.20) = (280 + x)(0.40)
Solving for x,
x = 160 mL of 75% alcohol mixture used
2) Let R be the amount of the Rift Valley coffee and H be that of the House coffee.
8.40R + 14.70H = 40(11.08)
R + H = 40
Solving these 2 equation simultanneously,
R = 22.984
H = 17.016