Answer: Let's denote the number of cubic centimeters of the 20% salt solution as x and the number of cubic centimeters of the 60% salt solution as y.
We know that the total volume of the mixture is 100 cubic centimeters, so we have:
x + y = 100
We also know that the final solution should be a 30% salt solution. This means that the amount of salt in the final solution should be 0.3 times the total volume of the solution:
0.3(100) = 0.20x + 0.60y
where 0.20x represents the amount of salt in the 20% salt solution and 0.60y represents the amount of salt in the 60% salt solution.
We now have two equations with two unknowns:
x + y = 100
0.20x + 0.60y = 30
We can solve for x and y by using any method of linear equations, such as substitution or elimination.
Here, we will use substitution. Solving the first equation for x, we get:
x = 100 - y
Substituting this expression for x in the second equation, we get:
0.20(100 - y) + 0.60y = 30
Simplifying and solving for y, we get:
20 - 0.20y + 0.60y = 30
0.40y = 10
y = 25
So, we need 25 cubic centimeters of the 60% salt solution.
To find the amount of the 20% salt solution, we can substitute this value of y back into either equation:
x + y = 100
x + 25 = 100
x = 75
So, we need 75 cubic centimeters of the 20% salt solution.
Therefore, we need to mix 75 cubic centimeters of the 20% salt solution and 25 cubic centimeters of the 60% salt solution to obtain 100 cubic centimeters of a 30% salt solution.