For a certain experiment, a student requires 100 cubic centimeters of a solution that is 8% HCI. The storeroom has only solutions that are 15% HCI and 5% HCI. How many cubic centimeters of each available solution should be mixed to get 100 cubic centimeters of 8% HCI?
Lets say x is the # of cubic centimeters of 15% HCI and 100-x is the # of cubic centimeters of 5% HCI.
0.15x + 0.05(100-x) = 0.08(100)
Solve it from there.
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To solve this problem, we can use a system of equations.
Let's assume x represents the volume of 15% HCl solution in cubic centimeters, and y represents the volume of 5% HCl solution in cubic centimeters.
According to the problem, the student wants to obtain 100 cubic centimeters of an 8% HCl solution. This means that the sum of the volumes of the two solutions should be equal to 100:
x + y = 100 ----(equation 1)
The student also needs to determine the specific volumes of each solution that should be mixed to get the desired concentration of 8% HCl. This means that the sum of the HCl content from each solution should be equal to 8% of the total volume (100 cubic centimeters):
(0.15x + 0.05y) = 0.08 * 100 ----(equation 2)
Now we can solve the system of equations using the method of substitution.
From equation 1, we can express x as follows:
x = 100 - y
Substituting this value of x into equation 2, we get:
(0.15(100 - y) + 0.05y) = 8
Simplifying the equation:
15 - 0.15y + 0.05y = 8
Combining like terms:
-0.1y = -7
Dividing by -0.1:
y = -7 / -0.1
y = 70
Substituting this value of y back into equation 1 to find x:
x = 100 - 70
x = 30
Therefore, the student should mix 30 cubic centimeters of a 15% HCl solution with 70 cubic centimeters of a 5% HCl solution to obtain 100 cubic centimeters of an 8% HCl solution.
To solve this problem, we can use a technique called the method of mixtures. Let's break down the problem step by step to determine the quantities needed.
Let's assume that x cubic centimeters of the 15% HCI solution is mixed with (100 - x) cubic centimeters of the 5% HCI solution to obtain 100 cubic centimeters of an 8% HCI solution.
Step 1: Determine the amount of HCI in the 15% solution and the 5% solution.
- The 15% HCI solution contains 15% HCI, which means that for every 100 cubic centimeters, there is 15 cubic centimeters of HCI.
- The 5% HCI solution contains 5% HCI, which means that for every 100 cubic centimeters, there is 5 cubic centimeters of HCI.
Step 2: Set up an equation based on the amount of HCI in the resulting 8% HCI solution.
- Since we need 100 cubic centimeters of a solution that is 8% HCI, there will be 8 cubic centimeters of HCI in the final solution.
Step 3: Use the equation to solve for the unknown variable.
- Based on the equation, we can determine that 15x/100 + 5(100 - x)/100 = 8.
- Simplify the equation: 15x + 500 - 5x = 800.
- Combine like terms: 10x + 500 = 800.
- Subtract 500 from both sides: 10x = 300.
- Divide both sides by 10: x = 30.
So, to obtain 100 cubic centimeters of an 8% HCI solution, mix 30 cubic centimeters of the 15% HCI solution with (100 - 30) = 70 cubic centimeters of the 5% HCI solution.