Bilbo asked in Science & MathematicsMathematics · 1 month ago

# Mixture word problem?

If you have 10pints of 40% solution and 10 pints of 20% solution and mix them together, what is the percentage?

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• 1 month ago

30%

In 10pints of 40% solution, there are 4 pints of solute (substance dissolved).

In 10pints of 20% solution, there are 2 pints of solute.

When you mix them together, you get 20 pints of a solution with 4+2=6pints of solute in it.

6/20=0.3 = 30%

• cosmo
Lv 7
1 month ago

It depends on the miscibility of the solutions.

• Philip
Lv 6
1 month ago

Solution 1 = 4 pints of ingredient A +  6 pints of ingredient B. Total pints = 10.;

Solution 2 = 2 pints of ingredient A +  8 pints of ingredient B. Total pints = 10.;

Solution 3 = 6 pints of ingredient A +14 pints of ingredient B. Total pints = 20.;

We assume all solutions only contain active ingredients A& B.;

Fraction of ingredient A in solution 3 = (6/20) = 100(6/20)% = 30%.;

Fraction of ingredient B in solution 3 = (14/20) = 100(14/20)% = 70%.;

• 1 month ago

20 pints 30% solution             .

• Jim
Lv 7
1 month ago

cV + cV = cV final

10pt (.40) + 10pt (.20) = (4+2 concetrate) in 20 pints

or 6/20 is 20 pints of 30% solution

• 1 month ago

If you have 10 pints of 40% solution and 10 pints of 20% solution

and mix them together, you will have 20 pints of 30% solution.

• Anonymous
1 month ago

Common sense ought to suggest it is 30%

And it is - In the first mix you have 4 pints of whatever it is in 10 and in the second mix 2 pints of it in 10. So combined you have 6 pints in 20, which makes 30%

• ted s
Lv 7
1 month ago

20 pints of 30%

• 1 month ago

40% of 10 pints = 4 pints

20% of 10 pints = 2 pints or 6 pints

Add 6 pints to 10+10=20 pints: 100% * 6/20 = 30%

• 1 month ago

Let x = amount of 40% solution

Let y = amount of 20% solution

So the total amount of the solution is: x + y

If you only want the volume of the substance that is dissolved, then the amount in the 40% solution is:

0.4x

and the amount in the 20% solution is:

0.2y

The total amount is then:

0.4x + 0.2y

Which is then equal to an unknown percentage (z) of the total volume:

0.4x + 0.2y = z(x + y)

We know what x and y are, 10 pints each.  So we can substitute what we know and solve for the remaining unknown: z:

0.4(10) + 0.2(10) = z(10 + 10)

4 + 2 = 20z

6 = 20z

z = 6/20

z = 0.3

The result is a 30% solution.