A mother has given her children candy. She gave her daughter half of all the candy and 1 additional, and her son - half of the left candy and 3 additional. How many candy did the mother give to her children?

I assume:

x - all the candy;

she gave to her daughter: $\displaystyle \frac{x}{2}+1$;

she gave to her son: $\displaystyle \frac{x-(\frac{x}{2}+1)}{2}+3$

BUT x is all the candy, but I need only the number of given to her children...