Grandmother whose age digits are her grandkids

A grandmother has two grandchildren whose ages are exactly the two digits of her own age (one is the tens digit, the other the units digit). The three ages add up to $98$. How old is the grandmother?

$85$. With digits $x$ (tens) and $y$ (units), $10x+y+x+y=11x+2y=98$. Only $x=8$, $y=5$ works with single digits, so she is $85$ (and $85+8+5=98$).