Question 1022936
Ages are 

X,X+1,X+2.........X+9 

This adds to 10X+45

10X+45=180

10X=135 or X=13.5, so, we have ages 

13.5 , 14.5 ....... 22.5, but such  problem calls for integers, we need to add .5 to top 5 ages, and subtract .5 from bottom 5.

13,14,15,16,17,19,20,21,22,23

Alice is 23, and can't be younger as that would force another child to be older. And no lower age is available to her.