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...
Hello, Evaldas!
I agree with you . . . The problem is not clearly stated.
It should have been more precise.
A mother has given her children candy.
She gave her daughter half of all the candy and 1 additional piece,
and gave her son half of the remaining candy and 3 additional pieces.
How many candys did the mother give to her children?
I assume: .$\displaystyle x$ = all the candy.
She gave to her daughter: .$\displaystyle \tfrac{x}{2}+1$
She gave to her son: .$\displaystyle \frac{x-(\frac{x}{2}+1)}{2}+3$
But $\displaystyle x$ is all the candy,
and I need only the number of given to her children.
It should have said:
. . "A mother has given her two children all of her candy."
There could have been other children who received their shares of the candy.
Are we to assume that all the candy was distributed to the daughter and son?
. . Recall that: $\displaystyle \text{ASSUME} \,=\,\text{ASS-U-ME}$
With this assumption, we have: .$\displaystyle \left[\frac{x}{2}+1\right] + \left[\frac{x-(\frac{x}{2}+1)}{2} + 3\right] \;=\;x$
. . from which we get: .$\displaystyle x \,=\,14$
She didn't give her two children all the candy, she gave some amount of candy. Her daughter she gave half of all the candy plus one additional (not from another pile of candy, from the same x (x-all candy)), and her son - half that's left after giving to her daughter plus 3 (also from the same x)....
So I'd say that she gave her children x-z=y amount of candy, or something like that.
This is my translation of the exercise into English...
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Originally Posted by Evaldas 
