Chemistry Help?

Question

How much of a 30% alcohol solution must be mixed with 8 liters of a 45% solution in order to get a mixture which is 42% alcohol. PLEASE explain, i don't know how to solve it.

Answer 1

Let A=the amount of alcohol in the solution
x is the amount of 30% solution that we are trying to find

8 (0.45 Liters A) ==> in the 8L container, 45% of it is alcohol.
8 + x is the total amount of solution in the end
42% of that total solution has alcohol in it ==>
(8 + x)(0.42 Liters A)

x(0.3 Liters A) + 8 (0.45 Liters A) = (8 + x)(0.42 Liters A)

0.3x + 0.45*8 = 0.42(8+x)
0.3x + 3.6 = 0.42x + 3.36
3.6 - 3.36 = 0.42x - 0.3x
0.24 = 0.12x
2 = x

You need 2 liters of the 30% solution to reduce 8 L of 45% solution to 42%.

Answer 2

I am pretty sure the answer is 3.666 liters and here is how I came up with that.

There are two solutions. One of 30% and the other of 45%. Write these as decimals 0.3 and 0.45. Ok, now there is 8 liters in one and volume of the other we will call x. The resulting solution we know is 0.42 and now we can say has a volume of (8 + x).... so putting it all together we get,

0.3*x + 0.45*8 = 0.42*(8+x)

Ok, solve this for x...
distribute the right side then combine like terms across the equation;
0.3x - 0.42x = 0.42(8) - 0.45(8)

Solve,
-.12x = -.44
x = 3.666 Liters

I hope this helps : )

Answer 3

(x liters)*(30%) + (8 liters)*(45%) = (x+8 liters)*(42%)

and solve for x

30% = 0.30, 45% = 0.45, 42% = 0.42, so:

0.30x + 0.45*8 = 0.42*(x+8)
0.30x + 3.6 = 0.42x + 3.36
3.6 - 3.36 = 0.42x - 0.30x
0.24 = 0.12x
2.0 = x

So you need two liters of 30%.

(Note -- Bear, in the post above, made an arithmetic error: 0.42 * 8 - 0.45*8 = 0.24, not 0.44)