SOLUTION: The age of Sarah is 14 less than three times the age of Ruth. The square root of Sarah's present age increased by 1 is equal to the square root of Ruth's age fifteen years from now

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: The age of Sarah is 14 less than three times the age of Ruth. The square root of Sarah's present age increased by 1 is equal to the square root of Ruth's age fifteen years from now      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 936145: The age of Sarah is 14 less than three times the age of Ruth. The square root of Sarah's present age increased by 1 is equal to the square root of Ruth's age fifteen years from now. Find their present ages.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Sarah's age now
Let +r+ = Ruth's age now
--------------------------
(1) +s+=+3r+-+14+
(2) ++sqrt%28+s+%2B+1+%29+=+sqrt%28+r+%2B+15+%29+
---------------------------------
Square both sides of (2)
(2) +s+%2B+1+=+r+%2B+15+
(2) +s+-+r+=+14+
and, from (1):
(1) +-s+%2B+3r+=+14+
---------------------
Add the equations
(2) +s+-+r+=+14+
(1) +-s+%2B+3r+=+14+
--------------------
+2r+=+28+
+r+=+14+
and, since
(1) +s+=+3r+-+14+
(1) +s+=+3%2A14+-+14+
(1) +s+=+28+
---------------
Ruth is 14
Sarah is 28
-----------
check:
(2) ++sqrt%28+s+%2B+1+%29+=+sqrt%28+r+%2B+15+%29+
(2) ++sqrt%28+28+%2B+1+%29+=+sqrt%28+14+%2B+15+%29+
(2) +sqrt%2829%29+=+sqrt%2829%29+
OK
(1) +s+=+3r+-+14+
(1) +28+=+3%2A14+-+14+
(1) +28+=+42+-+14+
(1) +28+=+28+
OK
----------------------