maths or chemistry problem?

Question

you need a 40% sol.(1000ml).you have a 70% sol. and a 20% sol. available.how much of each sol. will you need?

please show me your work

Answer 1

This is a math problem dealing with percentages.

First off you need to know how much of the solution you want: 40% of 1000 is 400.

So now you create two equations:

x = 70% solution in ml
y = 20% solution in ml

x+y = 1000
.70x + .20y = 400

Now all you need to do now is solve for x and y and there you go.

Answer 2

OK, say you have 1000 mL of the 70% solution. (I know, you won't need that much--but it's easier to work with round numbers while we work out the ratio.) That's 700 mL of the compound of interest and 300 mL of water.

Now, whenever you add a mL of the 20% solution, you are adding 0.8 mL of water and 0.2 mL of the compound. The percent concentration is (mL of compound/total mL)*100. So if x is the number of mL of 20% solution you have added, and c is the concentration, then C = (700 + 0.2x)/(1000 + x)*100. You want C to equal 40%, so 40 = (700 + 0.2x)/(1000 + x)*100.

Start by dividing both sides by 100. You get 0.4 = (700 + 0.2x)/(1000 + x)

Next, multiply both sides by 1000 + x. On the right side that cancels, leaving 700 + 0.2x. On the left side, it gives 400 + 0.4x. So now you have 400 + 0.4x = 700 + 0.2x.

Now subtract 400 and 0.2x from each side. That gives 0.4x - 0.2x = 700 - 400. That simplifies to 0.2x = 300.

Now divide by 0.2 to get x = 1500. For each liter of 70% solution, you need to add 1500 liters of 20% solution.

Since that will make 2500 mL and you need 1000, divide by 2.5. In other words, use 1000/2.5 mL of 70% and 1500/2.5 mL of 20%. That works out to 400 mL of 70% and 600 mL of 20%.

Final Answer: 400 mL of 70%, 600 mL of 20%.

Edit: OK, the person who answered while I was typing this had a more efficient way to solve it.

Answer 3

Let x represent the unknown amount of the 70% solution. Then 1-x represents the remaining 20% solution(100%-unknown).
x(0.70) + (1-x)(0.20) = 0.40
0.7x + 0.2 - 0.2x = 0.4
0.5x = 0.4-o.2=0.2
x = (0.2)/(0.5) = 0.4 or 40%
1-x = 1-o.4 =0.6 or 60%
So you need 40% or 400ml(0.4x1000ml)of the 70% solution and 60% or 600ml(0.6x1000ml) of the 20% solution.