Let's assign the quantity of the 10% sucrose solution Fred needs to use as "x" (in ml).
Since the total desired volume of the 15% sucrose solution is 45ml, the amount of the 25% sucrose solution needed would be the remaining volume, which is (45 - x) ml.
To determine the sucrose quantities in the final mixture, we can set up the following equation:
0.10x + 0.25(45 - x) = 0.15(45)
Simplifying the equation:
0.10x + 11.25 - 0.25x = 6.75
Combining similar terms:
-0.15x = -4.5
Dividing both sides by -0.15:
x = (-4.5) / (-0.15) = 30
Therefore, Fred should use 30ml of the 10% sucrose solution and (45 - 30) = 15ml of the 25% sucrose solution to obtain the desired 45ml of the 15% sucrose solution.