SOLUTION: Alex is 8 years younger than his sister. His mother is 6 years more than twice of his sister’s age. His mother is 42 years old. Find the ages of Alex and his sister.

Algebra ->  Human-and-algebraic-language -> SOLUTION: Alex is 8 years younger than his sister. His mother is 6 years more than twice of his sister’s age. His mother is 42 years old. Find the ages of Alex and his sister.      Log On


   

Question 203209: Alex is 8 years younger than his sister. His mother is 6 years more than twice of his sister’s age. His mother is 42 years old. Find the ages of Alex and his sister.
Found 2 solutions by Earlsdon, jojo14344:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let M = Mother's age.
A = Alex's age.
S = Sister's age.
A = S-8
M = 2S+6
M = 42, so...
2S+6 = 42 Subtract 6 from both sides.
2S = 36 Divide both sides by 2.
S = 18
A = 18-8 = 10
Alex is 10 years old and his sister is 18 years old.

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Note the following:

Sister's Age = x -----> A
Alex's Age = x-8yrs --> B
Mother's Age = 6%2B2x --> C

Since Mother's age is given = 42+yrs, we can equate to C.
6%2B2x=42yrs
2x=42-6=36 ---> cross%282%29x%2Fcross%282%29=cross%2836%2918%2Fcross%282%29
red%28x=18yrs%29, Sister's Age

Alex's Age= highlight%2818%29-8=red%2810yrs%29

To check,
Mother's Age = 6%2B2%2818%29=6%2B36=red%2842yrs%29 ---> twice Sister's age,2%2A18=36yrs + 6, 36%2B6=42yrs

Thank you.
Jojo