A solution is mixed with a 12% acid solution to form a 16% acid solution. How many liters of the 20% acid solution are used to make 10 liters of the 16% acid solution?
V*.2+(10-V).12=10*.16
Thanks. i worked it out and it came out to = 4 liters
is it 4 liter???
To find the number of liters of the 20% acid solution needed, we can break down the problem into two equations:
Let's assume that x liters of the 20% acid solution are used.
Equation 1: The total volume of the final solution is 10 liters
x + (10 - x) = 10
Equation 2: The acid content in the final solution is 16%
(0.2x + 0.12(10 - x)) / 10 = 0.16
Let's solve these equations step by step:
Step 1: Solve Equation 1 for x:
x + 10 - x = 10
10 = 10
Step 2: Simplify Equation 2:
(0.2x + 1.2 - 0.12x) / 10 = 0.16
(0.08x + 1.2) / 10 = 0.16
0.08x + 1.2 = 0.16 * 10
0.08x + 1.2 = 1.6
Step 3: Subtract 1.2 from both sides:
0.08x = 1.6 - 1.2
0.08x = 0.4
Step 4: Divide both sides by 0.08 to solve for x:
x = 0.4 / 0.08
x = 5
Therefore, 5 liters of the 20% acid solution are needed to make 10 liters of the 16% acid solution.