SOLUTION: Three years ago,Ali was eight times as old as Adi.Three years from now,Ali will only be five times as old as Adi.Find their present ages.

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Question 1185604: Three years ago,Ali was eight times as old as Adi.Three years from now,Ali will only be five times as old as Adi.Find their present ages.
Found 2 solutions by math_helper, greenestamps:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!




Let L = Ali's age now

and D = Adi's age now



From the 3yrs ago info:

(1)  L-3 = 8(D-3)  -->  L = 8D-21



From the 3yrs from now info:

(2)  L+3 = 5(D+3)  -->  L = 5D+12



L=L -->  8D-21 = 5D+12 



Solve this to get  D=11  (Adi is 11)

Plug D=11 into (1) or (2) and solve for L:  L = 67   (Ali is 67)



Check:

67-3 = 64 

8(11-3) = 64  (ok, using 3yrs ago info)



67+3 = 70

5(11+3) = 70  (ok, using 3yrs from now info)

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution from the other tutor is fine....

Here is a different way to solve the problem with a different setup.

Given that Ali was 8 times as old as Adi 3 years ago...

Let x = Adi's age 3 years ago
Then 8x = Ali's age 3 years ago

Given that Ali will be 5 times as old as Adi 3 years from now (6 years after 3 years ago)...

x+6=Adi's age 3 years from now
8x+6=Ali's age 3 years from now

8x+6=5(x+6)
8x+6=5x+30
3x=24
x=8

Their ages 3 years ago were x=8 and 8x=64; their ages now are 11 and 67.

ANSWERS: Adi is now 11; Ali is now 67