SOLUTION: ) The ratio of ages of mother and son is 2:1 Mother was 30 years old when she gave birth to her only daughter who is 5 years younger to her only son. Find the present age of mother

Question 519630: ) The ratio of ages of mother and son is 2:1 Mother was 30 years old when she gave birth to her only daughter who is 5 years younger to her only son. Find the present age of mother.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
m = mother's age
s = son's age
d = daughter's age
.
Today, ratio of mother's age to son's age is 2:1.
m = 2s
.
The son is 5 years older than the daughter, so when d was born, s was 5.
That is d=0 when she is born and s=5
We're told the mother was 30 then.
.
However, the ratio of mother's to son's ages is unknown at that point in time. It's 2:1 today.
.
Logically, we know that x years later, which is the current day, the ratio is 2:1
.
30+x = 2(5+x)
.
30 + x = 10 + 2x
.
20 = x
x = 20
.
That means 20 years have gone by.
.
m = 30+20 = 50 years old = mother's present age
.
s = 5+20 = 25 years old, which satisfies the 2:1 ratio.
.
d = 25-5 = 20, if anyone wants to know how old the daughter is.
.
Done.
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