How many mL of water at 10C must be added to 75mL of water at 35C to obtain a final temperature of 19C?

Use the formula Q = mcT.

A certain quantity of heat Q has to be supplied to the water at 10 C and that same amount of heat has to be lost by the water at 35 C. Therefore you equate the two as follows:

Q_{35} = -Q_{10}

m_{35}cT = -m_{10}cT

T is the temperature change, so, the water at 35 has to decrease from 35 to 19, and that of 10C from 10 to 19. The mass of water is 75 mL, and the specific heat capacity is the same for both, and thus, they cross out each other.

(75)\cancel{c}(35-19) = -m_{10}\cancel{c}(10-19)

(75)(35-19) = -m_{10}(10-19)

Can you solve the problem now? :)