SOLUTION: Five years ago I was thrice as old as my son and ten years later I shall be twice as old as my son. How old are we now?

Question 953630: Five years ago I was thrice as old as my son and ten years later I shall be twice as old as my son. How old are we now?

Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
Five years ago I was thrice as old as my son and ten years later I shall be twice as old as my son. How old are we now?
M=my age; S=son's age
M-5=3(S-5)
M-5=3S-15 Add 15 to each side.
(M+10)=3S Divide each side by 3.
(M+10)/3=S Use this to substitute for S.
SITUATION A:If ten years later is later than 5 years ago:
M+5=2(S+5)
M+5=2S+10 Subtract 10 from each side.
M-5=2S Substitute for S.
M-5=2((M+10)/3)
M-5=(2M+20)/3 Multiply each side by 3.
3M-15=2M+20 Add 15 to each side.
3M=2M+35 Subtract 2M from each side.
M=35 ANSWER 1A: My age is 35 years old.
2S=M-5 Divide each side by 2.
S=(M-5)/2
S=(35yrs-5yrs)/2
S=30yrs/2=15yrs ANSWER 2A: The son is 15 years old.
SITUATION B:If ten years later is later than now:
M+10=2(S+10)
M+10=2S+20 Subtract 20 from each side
M-10=2S Substitute for S
M-10=2((M+10)/3)
M-10=(2M+20)/3 Multiply each side by 3.
3M-30=2M+20 Add 30 to each side.
3M=2M+50 Subtract 2M from each side.
M=50 ANSWER 1B: My age is 50 years old
2S=M-10
S=(M-10yrs)/2=(50yrs-10yrs)/2=40yrs/2=20 yrs ANSWER 2B: The son is 20 years old.
PLEASE IN THE FUTURE TRY TO BE LESS AMBIGUOUS STATING THE QUESTION.
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