A chemist needs 12 L of a 40% alcohol solution. She must mix a 20% solution and

Question

A chemist needs 12 L of a 40% alcohol solution. She must mix a 20% solution and a 50% solution. How many liters of each will be required to obtain what she needs? The owner of a tea shop wants to mix three kinds of tea to make 100 oz of a mixture that will sell for $0.83 per oz he uses orange Pekoe, which sells for $0.80 per oz, Irish breakfast, for $0.85 per oz, and earl Grey, for $0.95 per oz. If he wants to use twice as much Orange Pekoe as Irish Breakfast, how much of each kind of tea should he use?

Explanation / Answer

24) 12 litres of 40% solution is requried and he was a 20% solution and a 50% solution.
Given that 40% is 10% away from 50% and 40% is 20% away from 20% we can safely say that the quantity of 50% solution required will be twice as much as the quantity of 20% solution.
So 12 litres has to be distributed as 2x litres of 50% and x litres of 20% so total of 3x litres = 12 litres so x=12/3 = 4 litres.
hence quantity of 20% solution = 4 litres and quantity of 50% solution = 4*2=8 litres.

Verification : total quantity of alcohol = 4*0.2 + 8*0.5 = 0.8+4 = 4.8 ; so 4.8/12 = 0.4 which is our deisred 40%

25)
100 oz of 0.83$ mixture is to be obtained from 0,80$ OP, 0.85$ IB and 0.95$ EG.
Also it is given that OP= 2IB =2x we have the equation
2x+x+y = 100
2x*0.80 + x*0.85 + y*0.95 = 0.83*100 = 83
3x+y=100
1.6x+ 0.85x+0.95y = 83 which is 2.45x + 0.95y = 83
Solving 3x+y = 100 and 2.45x+0.95 y =83
Multiply 3x+y=100 with 0.95 on both sides, we get
2.85x + 0.95y = 95
Subtract from this equation 2.45x+0.95y= 83
we get :
0.4x =12 so x=12/0.4 = 120/4=30
3x+y=100 so 3*30 + y = 100
y= 100-90 = 10 litres
So the quantity of Orange Pekoe = 2x = 60 litres
Quantity of Irish Breakfast = x = 30 litres
Quantity of Early Grey = y = 10 litres

Verification Orange Pekoe is indeed twice as Irish Breakfast since 60=2*30 and
60*0.80 + 30* 0.85+10*0.95 =   48+25.5+9.5 = 48+35 = 83 upon dividing it by 100 oz we get = 0.83$ as selling price per oz.

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