SOLUTION: When a really smart kid was asked about his mother's age, he said: "i am a fifth as old as my mother. In six years i will be one third as old" How old iss the kid and his mother?

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: When a really smart kid was asked about his mother's age, he said: "i am a fifth as old as my mother. In six years i will be one third as old" How old iss the kid and his mother?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1050652: When a really smart kid was asked about his mother's age, he said: "i am a fifth as old as my mother. In six years i will be one third as old"
How old iss the kid and his mother?
Found 3 solutions by addingup, josmiceli, MathTherapy:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
Son = 1/5Mother
S+6 = 1/3(M+6) Substitute for Son
1/5M+6 = 1/3(M+6)
1/5M+6 = 1/3M+2
1/5M = 1/3M-4
1/5M-1/3M = -4
3/15M-5/15M = -4
-2/15M = -4 Divide both sides by 2/15 and remember -/- = +
M = -4/(-2/15) To divide by fraction invert and multiply
M = (4*15)/2
M = 30 The mother is 30 years old
S = 1/5M = 1/5*30 = (1*30)/5 = 6 The son is 6 years old
---------------------------
Check:In 6 years
30+6 = 36
6+6 = 12
1/3 of 36: 1/3*36 = (1*36)/3 = 12 Correct
:
John

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = kid's present age
Let +b+ = mother's present age
--------------------------------
(1) +a+=+%281%2F5%29%2Ab+
(2) +a+%2B+6+=+%281%2F3%29%2A%28+b+%2B+6+%29+
----------------------------------
(1) +b+=+5a+
(2) +3a+%2B+18+=+b+%2B+6+
(2) +b+=+3a+%2B+12+
Substitute (1) into (2)
(2) +5a+=+3a+%2B+12+
(2) +2a+=+12+
(2) +a+=+6+
and
(1) +b+=+5a+
(1) +b+=+5%2A6+
(1) +b+=+30+
----------------
The kid is 6
The mother is 30
-------------------
check:
(2) +a+%2B+6+=+%281%2F3%29%2A%28+b+%2B+6+%29+
(2) +6+%2B+6+=+%281%2F3%29%2A%28+30+%2B+6+%29+
(2) +12+=+%281%2F3%29%2A36+
(2) +36+=+36+
OK

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

When a really smart kid was asked about his mother's age, he said: "i am a fifth as old as my mother. In six years i will be one third as old"
How old iss the kid and his mother?
let son's age be S

Then mother's is: 5S

We then get: 5S + 6 = 3(S + 6)

Solve to get: