Answer:
40/7 liters of 5% acid, 30/7 liters of 40% acid
Step-by-step explanation:
We need to find a value so that the amount of acid is 20% = 1/5 of the total amount of liquid. Therefore, if x represents the total amount of liquid, we can say that
1/5 (x) = amount of acid at the end
We know that we need 10 liters of solution, so
1/5 (10) = amount of acid at the end = 2 liters
If we have y amount of 5% = 0.05 acid solution and z amount of 40% =0.4 acid solution, the total amount of acid will be equal to
0.05 * y (amount of acid from 0.05 acid solution) + 0.4 * z = 2
Next, we know that the total amount of liters is 10, and the liters come from the 5% and 40% acid solutions, so
y + z = 10
We therefore have
0.05 * y + 0.4 * z = 2
y + z = 10
One way to solve this is to solve for z in the second equation and plug that into the first.
subtract y from both sides in the second equation to isolate z
10 -y = z
plug 10-y in for z in the second equation
0.05 * y + 0.4 * (10-y) = 2
0.05 * y + 4 -0.4 * y = 2
-0.35 * y + 4 = 2
subtract 4 from both sides to isolate the y and its coefficient
-0.35y = -2
divide both sides by -0.35 to isolate y
y = -2/-0.35 = 40/7 * (-0.05/-0.05) = 40/7 liters
z = 10 - y = 10-40/7 = 70/7 - 40/7 = 30/7 liters
