Given that the amount of heat given to a system be $\left(dQ\right) = 50 \mathrm{J}$ and work done on the system be $\left(dW\right) = -15 \mathrm{J}$

Here, $dQ=50 \mathrm{J}, dW=-15 \mathrm{J}$
from the first law of thermodynamics,$dQ=dU+dW \to \left(1\right)$

 the change in internal energy of the system is
$dU=dQ-dW=50-\left(-15\right)=65\mathrm{ }\mathrm{J}$