how many litres of a solution containing 18 percent sulfuric asid and how many litres of another solution containing 25 percent sulfuric asid must mixed together to make 550 litres solution containing 23 percent of sulfuric acid
Vl is volume of 18 percent
Vh is volume of 25 percent
Vl+Vh=550
.18*Vl+.25*Vh=.23*550
does this help?
To find the quantities of each solution needed, we can follow these steps:
Step 1: Let's assume the volume of the solution containing 18% sulfuric acid as x liters.
Step 2: Therefore, the volume of the solution containing 25% sulfuric acid would be (550 - x) liters.
Step 3: In the first solution, the sulfuric acid content is 18% of x liters, which can be expressed as 0.18x liters.
Step 4: In the second solution, the sulfuric acid content is 25% of (550 - x) liters, which can be expressed as 0.25(550 - x) liters.
Step 5: The total sulfuric acid content in the mixed solution should be 23% of 550 liters, which can be expressed as 0.23 * 550 liters.
Step 6: Now, we can set up an equation based on the sulfuric acid content:
0.18x + 0.25(550 - x) = 0.23 * 550
Step 7: Solve the equation to find the value of x:
0.18x + 137.5 - 0.25x = 126.5
-0.07x = -11
x = 157.14 liters (approx.)
Step 8: Substitute the value of x into the equation to find the volume of the second solution:
550 - x = 550 - 157.14 = 392.86 liters (approx.)
Therefore, approximately 157.14 liters of the solution containing 18% sulfuric acid and approximately 392.86 liters of the solution containing 25% sulfuric acid should be mixed together to make a 550 liters solution containing 23% sulfuric acid.
To solve this problem, we need to use the concept of mixture problems and express the given information in equations.
Let's assume we need to mix x liters of the 18% sulfuric acid solution with y liters of the 25% sulfuric acid solution to obtain a final solution of 550 liters containing 23% sulfuric acid.
The amount of sulfuric acid in the 18% solution is 18/100 * x liters, and the amount of sulfuric acid in the 25% solution is 25/100 * y liters.
Therefore, the total amount of sulfuric acid in the final solution is (18/100 * x) + (25/100 * y) liters.
According to the problem, the final solution must contain 550 liters and have 23% sulfuric acid, so we can write the equation:
(18/100 * x) + (25/100 * y) = 23/100 * 550
Simplifying the equation:
0.18x + 0.25y = 0.23 * 550
Multiply both sides of the equation by 100 to remove the decimal points:
18x + 25y = 12650
Now, we have a system of equations to solve:
18x + 25y = 12650 --(1)
x + y = 550 --(2)
There are multiple ways to solve this system of equations, such as substitution or elimination method. Let's use the substitution method.
Rearrange equation (2) to express x in terms of y:
x = 550 - y
Now substitute this value of x in equation (1):
18(550 - y) + 25y = 12650
Simplify the equation:
9900 - 18y + 25y = 12650
Combine like terms:
7y = 2750
Divide both sides of the equation by 7:
y = 2750/7
y ≈ 392.86
Now, substitute the value of y back into equation (2) to find x:
x + 392.86 = 550
x = 550 - 392.86
x ≈ 157.14
Therefore, to make a 550-liter solution containing 23% sulfuric acid, you need to mix approximately 157.14 liters of the 18% sulfuric acid solution with approximately 392.86 liters of the 25% sulfuric acid solution.