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?"

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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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = Manuel's age now
Let +s+ = his sister's age now
------------------------------
given:
(1) +m+=+s+%2B+8+
(2) +m+-+3+=+3%2A%28+s+-+3+%29+
-------------------------
By substitution:
(2) +s+%2B+8+-+3+=+3%2A%28+s+-+3+%29+
(2) +s+%2B+5+=+3s+-+9+
(2) +2s+=+14+
(2) +s+=+7+
and
(1) +m+=+s+%2B+8+
(1) +m+=+7+%2B+8+
(1) +m+=+15+
------------------
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