SOLUTION: Alex is 6 years older than Sara. Sixteen years ago, Alex was 1 1/2 times as old as Sara. How old are they now?

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Question 398133: Alex is 6 years older than Sara. Sixteen years ago, Alex was 1 1/2 times as old as Sara. How old are they now?
Found 2 solutions by ewatrrr, stanbon:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Alex is 6 years older than Sara

Let x and (x+6) represent the ages of Sara and Alex NOW respectively

Question states*** 16 years ago...

 (x+6) - 16 = 3/2(x-16)

solving for x

    x - 10 = 1.5x - 24

       14 = .5x

       14/.5 = x

         x = 28, Sara's age NOW.  Alex is 34 NOW.   (28 + 6)



CHECKING our Answer***

 18 = 1.5 * 12 = 18

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Alex is 6 years older than Sara. Sixteen years ago, Alex was 1 1/2 times as old as Sara. How old are they now?
---------
Equations:
a = s+6
(a-16) = (3/2)(s-16)
-----
Substitute for "a" and solve for "s":
(s+6-16) = (3/2)(s-16)
2(s-10) = 3s-48
2s-20 = 3s-48
s = 28 (Sara's age now)
----------------------
Solve for "a":
a = s+6
a = 28+6
a = 34 (Alex's age now)
============================
cheers,
Stan H.


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