SOLUTION: The sum of the present ages of Tahir and Masud is 18 years. Three years ago Tahir was three times as old as Masud. Find their present ages?

Question 1058736: The sum of the present ages of Tahir and Masud is 18 years. Three years ago Tahir was three times as old as Masud. Find their present ages?
Found 2 solutions by rothauserc, addingup:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Let T be Tahir's age and M be Masud's age
:
1) T + M = 18
:
2) (T-3) = 3 * (M-3)
:
solve equation 1) for T
:
T = 18 - M
:
substitute for T in equation 2)
:
18 - M - 3 = 3M - 9
:
add M to both sides of =
:
15 = 4M - 9
:
add 9 to both sides of =
:
4M = 24
:
M = 6
:
From equation 1) T = 18 - 6 = 12
:
*********************
Tahir is 12 years old
Masud is 6 years old
*********************
:

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
T+M = 18; T = 18-M
T-3 = 3(M-3)
T-3 = 3M-9
18-M-3 = 3M-9
15-M = 3M-9
-4M = -24 divide both sides by -4, and remember -/- = +
M = 6
Now solve for T:
T-3 = 3*(6-3)
T-3 = 9
T = 12
------------------------
Check:
6+12 = 18 Correct
Note: You can also solve for T:
T+M = 18; T+6 = 18; T = 12
and then check by substituting in
T-3 = 3(M-3); 12-3 = 3(6-3); 9 = 9 Correct
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