How many cubic centimeters of a 25% antibiotic solution sould be added to 10 cubic centimeters of a 60% antibiotic solution in order to get a 30% antibiotic solution?
Because x=60 trust me I did the math and search it up online
To find out how many cubic centimeters of a 25% antibiotic solution should be added to 10 cubic centimeters of a 60% antibiotic solution to achieve a 30% antibiotic solution, we can use the following steps:
Step 1: Assign variables to the unknowns:
Let x represent the amount (in cubic centimeters) of the 25% antibiotic solution that needs to be added.
Step 2: Express the initial amounts of the solutions:
We have 10 cubic centimeters of a 60% antibiotic solution.
Step 3: Express the final amount of the solution:
The final volume of the solution will be the sum of the volumes of the two solutions, which is 10 + x cubic centimeters.
Step 4: Write the equation based on the amounts and concentrations:
0.25x + 0.60(10) = 0.30(10 + x)
Step 5: Solve the equation:
0.25x + 6 = 3 + 0.30x
Subtract 0.25x from both sides:
6 - 3 = 0.30x - 0.25x
3 = 0.05x
Divide both sides by 0.05:
3/0.05 = x
60 = x
Therefore, 60 cubic centimeters of the 25% antibiotic solution should be added to 10 cubic centimeters of the 60% antibiotic solution to obtain a 30% antibiotic solution.
To find out how many cubic centimeters of a 25% antibiotic solution should be added to a 10 cubic centimeter of a 60% antibiotic solution to get a 30% antibiotic solution, we can use a method called the "mixture problem."
Let's break down the problem step by step:
Step 1: Determine the given information
- We have a 10 cubic centimeter of a 60% antibiotic solution.
- We want to add a certain amount of a 25% antibiotic solution.
- We need to achieve a final concentration of 30% antibiotic solution.
Step 2: Set up the equation
- Let's assume the amount (in cubic centimeters) of the 25% antibiotic solution to be added is x.
- The total volume of the resulting solution will be 10 + x cubic centimeters.
To calculate the final concentration, we need to consider the amount of antibiotic in the initial solution and the added solution. We have:
0.60 * 10 (cubic centimeters of the 60% solution) + 0.25 * x (cubic centimeters of the 25% solution) = 0.30 * (10 + x) (cubic centimeters of the resulting solution)
Step 3: Solve the equation
- Simplify the equation:
6 + 0.25x = 3 + 0.30x
0.25x - 0.30x = 3 - 6
-0.05x = -3
x = (-3) / (-0.05)
x = 60
So, you would need to add 60 cubic centimeters of the 25% antibiotic solution to the 10 cubic centimeters of the 60% antibiotic solution to get a 30% antibiotic solution.