A chemist needs 5 liters of a 70% alcohol solution.?

Question

A chemist needs 5 liters of a 70% alcohol solution. If she mixes a 90% alcohol solution and a 40% alcohol solution, how much of the 40% solution should she use?

It doesn't depend on how much of the 90% was used. I think that you have to use linear or nonlinear equations to figure this out but I don't know how to go about doing it. Please help!

Answer 1

We need x liters of 40% solution
We need (5-x) liters of 90% solution

x(40/100) + (5-x)*(90/100) = 5 * (70/100)
.40x + .90(5-x) = 5*.70
.40x + 4.5 - .90x = 3.5
.40x - .90x = 3.5 - 4.5
-.5x = -1
x = -1 / -.5
x = 2
2 gallons of 40% solution and 3 gallons of 90% solution.

To test our work:
2 gallons of 40% solution gives you 2 * .40 gallons of alcohol = .8
3 gallons of 90% solution gives you 3 * .90 gallons of alcohol = 2.7
.8 + 2.7 = 3.5 total gallons of alcohol, with 1.5 gallons of water (I assume water since it's not mentioned what the other substance would be).

3.5 / 5.0 = .70 or 70%

Answer 2

Let amount of 40%be x liters
Then amount of 90%is 5- x liters
Acc. To given condition
40*x/100+90*(5-x)/100=70*5/100
solve this for x

Answer 3

3L of 90% Alcohol + 2L of 40% Alcohol
= [(3*0∙9)+(2*0∙4)]/5
= [(2∙7)+(0∙8)]/5
= 3∙5/5
= 0∙7
≈ 70%

Answer 4

a million Litre (1000ml) of 70% alcohol answer contains 700ml of alcohol. 0.737 Litres (737ml) of ninety 5% alcohol answer contains 700ml of alcohol. that is an same honestly quantity of alcohol as you had on your unique 70% answer. you may upload as a lot non alcoholic liquid to this as you want and it is going to nonetheless really include 700ml of alcohol. excellent to a million Litre and also you've 700ml of alcohol in a 70% answer. excellent to 2 Litres and also you nonetheless really have 700ml of alcohol, although that's now a 35% answer.

Answer 5

V1C1 + V2C2 =VtCt
(5-x)(.9) + (X)(.4) = (5)(.7)

solve for x

you should get 2L 40% and 3L 90%

Answer 6

Well I would say that 100% of your question means you need to get out of the house more.