Question 1201295
<br>
I will guess that you have posted the problem exactly as it was given to you....<br>
Unfortunately, the wording makes the problem have no solution in non-negative integers, as is required in age problems.<br>
The difficulty is that "four times older than..." does not mean what nearly everybody thinks it means.  "Four times AS OLD AS" clearly means that if the one age is x then the other age is 4x.  But "four times OLDER THAN" means that if the one age is x then the other age is x+4x = 5x.<br>
And with the correct interpretation of the problem as you show it, the solution gives ages that are not integers.<br>
So almost certainly the intended information is that Alice is 4 times AS OLD AS Cindy.  Then we have<br>
x = Cindy
4x = Alice (4 times as old as Cindy)
4x+3 = Barbie (3 years older than Alice)<br>
The sum of their ages is 30:<br>
x+4x+4x+3 = 30
9x+3 = 30
9x = 27
x = 3<br>
ANSWER: Cindy is x=3 years old<br>