SOLUTION: Jack is nine years older than Tina. Jack is four times as old as Ali was three year ago. Ali is eighteen years younger than Jack. how old is tina

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Question 1129966: Jack is nine years older than Tina. Jack is four times as old as Ali was three year ago. Ali is eighteen years younger than Jack. how old is tina
Found 2 solutions by josmiceli, KMST:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Jack's age now
Let +b+ = Tina's age now
Let +c+ = Ali's age now
----------------------------------
(1) +a+=+b+%2B+9+
(2) +a+=+4%2A%28+c+-+3+%29+
(3) +c+=+a+-+18+
--------------------------
Substitute (3) into (2)
(2) +a+=+4%2A%28+a+-+18+-+3+%29+
(2) +a+=+4a+-+84+
(2) +3a+=+84+
(2) +a+=+28+
and
(3) +c+=+28+-+18+
(3) +c+=+10+
and
(1) +28+=+b+%2B+9+
(1) +b+=+19+
------------------------
Tina is 19
------------------------
check:
(2) +a+=+4%2A%28+c+-+3+%29+
(2) +28+=+4%2A%28+10+-+3+%29+
(2) +28+=+4%2A7+
(2) +28+=+28+
and
(3) +c+=+a+-+18+
(3) +10+=+28+-+18+
(3) +10+=+10+
and
(1) +a+=+b+%2B+9+
(1) +28+=+19+%2B+9+
(1) +28+=+28+
OK

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= Tina's age 19
x%2B9= Jack's age, because "Jack is nine years older than Tina."
%28x%2B9%29-18=x-9= Ali's age, because "Ali is eighteen years younger than Jack."
%28x-9%29-3=x-12= how hold Ali was the years ago
4%28x-12%29=4x-48= Jack's age, because "Jack is four times as old as Ali was three year ago."
We see that Jack's age is x%2B9 and 4x-48 , so
4x-48=x%2B9 is our equation.
Adding -x%2B48 to both sides of the equation,
4x-48-x%2B48=x%2B9-x%2B48 ,
and "collecting like terms" and simplifying, we get
3x=57
Dividing both sides of the equation by 3, we get
3x%2F3=57%2F3 , which simplifies to
highlight%28x=19%29 .

So, Tina is highlight%2819%29 ;
Jack is 19%2B9=28 ;
Ali is 28-18=10 ;
3 years ago Ali was 10-3=7 ,
and Jacks age is four times as much as that: 4%2A7=28 .