SOLUTION: can you help me solve the world problem "Manuel is 8 years older than his sister. Three years ago he was 3 times older than his sister. How old is each now?"

Question 959256: can you help me solve the world problem "Manuel is 8 years older than his sister. Three years ago he was 3 times older than his sister. How old is each now?"
Found 2 solutions by macston, josmiceli:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
M=Manuel's age; S=sister's age=M-8yrs
M-3yrs=3(S-3yrs) Substitute for S
M-3yrs=3(M-8yrs-3yrs)
M-3yrs=3M-33yrs Add 33yrs to each side.
M+30 yrs=3M Subtract M from each side.
30 yrs=2M Divide each side by 2.
15 yrs=M ANSWER 1: Manuel is 15 years old
S=M-8yrs=15yrs-8yrs=7yrs ANSWER 2: Sister is 7 years old
CHECK:
M-3yrs=3(S-3yrs)
15yrs-3yrs=3(7yrs-3yrs)
12yrs=3(4yrs)
12yrs=12yrs
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = Manuel's age now
Let = his sister's age now
------------------------------
given:
(1)
(2)
-------------------------
By substitution:
(2)
(2)
(2)
(2)
and
(1)
(1)
(1)
------------------
Manuel is 15
His sister is 7
-------------
check:
Manuel is 8 years older than his sister
true
3 years ago he was 12
3 years ago, his sister was 4
He was 3 times his sister's age
true

RELATED QUESTIONS
Manuel is 8 years older than his sister. 3 years ago he was 3 times older than his... (answered by ewatrrr)
Please help me solve: John is 4 years older than his sister, and 6 years ago he was... (answered by oberobic)
A man is 2 years older than his sister. Thirty years ago he was 3 times as old as her.... (answered by JulietG)
A man is 2 years older than his sister. Thirty years ago he was 3 times as old as her.... (answered by ankor@dixie-net.com)
fred is 3 times older than his sister Mary, four years ago he was 5 times as old as his... (answered by macston)
Age Problems Can you please help me write this into an equation. Seven years ago,... (answered by MathTherapy)
Please help me to solve this question 5 years ago amer was 10 years older than his... (answered by randyjoseph7,josmiceli)
Can you please help me solve this problems: 1.) Erwin is 5 times older than john and... (answered by mangopeeler07)
barry is 8 years older than his sister. in 3 years he will be twice as old as sue was 5... (answered by algebrahouse.com)