x mL of the 35% saline solution contains 0.35x mL of salt.
10 mL of the 75% solution contains 0.75 • 10 mL = 7.5 mL of salt.
After mixing, the scientist would have a total volume of (x + 10) mL. We know its concentration is 40%, so it contains 0.40 (x + 10) mL of salt.
The total amount of salt before and after mixing must be the same, so
0.35x + 7.5 = 0.40 (x + 10)
Solve for x :
0.35x + 7.5 = 0.40x + 4.0
0.10x = 3.5
x = 35
The scientist used 35 mL of the 35% solution.
