SOLUTION: The current age ratio of two girls is 1:3 after four years it will be 2:3, what is the current age of the older girl

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Question 951884: The current age ratio of two girls is 1:3 after four years it will be 2:3, what is the current age of the older girl
Found 2 solutions by ankor@dixie-net.com, KMST:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The current age ratio of two girls is 1:3 after four years it will be 2:3, what is the current age of the older girl
:
I don't this is possible, assuming the ages are integers, but let's try it
:
let x = the multiplier
then
1x = the age of one girl
3x = age of the older girl
:
%28%28x%2B4%29%29%2F%28%283x%2B4%29%29 = 2%2F3
Cross multiply
3(x+4) = 2(3x+4)
3x + 12 = 6x + 8
12 - 8 = 6x - 3x
4 = 3x
x = 4/3 is the multiplier
The younger girl is 4/3 which is 1 yr 4 months
then
3(4%2F3) = 4 yrs is the age of the older girl
:
Check this by finding their ages in 4yr
51%2F3 is the age in of the younger
8 yrs is the age of the older
:
Check the fraction using decimals on a calc 5.3333%2F8 = .6666 ~ 2%2F3
:
:
This means that when the younger is 1 yr 4 months, the older is 4 yrs old
Seems like they would at least have integer ages here.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There must be a typo, because as it is written it does not make sense.
The ages do not turn out to be whole numbers.
x= current age of the younger girl, and
y= current age of the older girl
"The current age ratio of two girls is 1:3" translates as
1%2F3=x%2Fy<--->y=3x , so
x= current age of the younger girl,
3x= current age of the older girl,
x%2B4= age of the younger girl after 4 years, and
3x%2B4= age of the older girl after 4 years.
The age ratio of two girls "after four years it will be 2:3" translates as
2%2F3=%28x%2B4%29%2F%283x%2B4%29<--->2%283x%2B4%29=3%28x%2B4%29<-->6x%2B8=3x%2B12<--> ,
and the older girl's age would be 3x=3%2A%284%2F3%29=4 .
Four years later, the older girl's age would be 4%2B4=8 ,
and the younger girl's age would be 4%2F3%2B4=4%2F3%2B12%2F13=16%2F3=5%241%2F3
Although the ratios are as required:
%28%284%2F3%29%29%2F4=1%2F3 and %28%2816%2F3%29%29%2F8=2%2F3 ,
ages are always truncated to whole number,
so 1%261%2F3 years after being born, a girl's age is said to be 1 ,
and 1%261%2F3 years after birth, she is said to be 5 years old.