SOLUTION: Please help me solve this equation:Daniel is three times as old as kathryn. seven years ago, daniel was five times as old as kathryn. How are old they?

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Question 1038595: Please help me solve this equation:Daniel is three times as old as kathryn. seven years ago, daniel was five times as old as kathryn. How are old they?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = Daniel's age now
Let +k+ = Kathryn's age now
-------------------------------
(1) +d+=+3k+
(2) +d+-+7+=+5%2A%28+k+-+7+%29+
---------------------------
This is 2 equations and 2 unknowns,
so it's solvable
Substitute (1) into (2)
(2) +3k+-+7+=+5%2A%28+k+-+7+%29+
(2) +3k+-+7+=+5k+-+35+
(2) +2k++=+35+-+7+
(2) +2k+=+28+
(2) +k+=+14+
and
(1) +d+=+3%2A14+
(1) +d+=+42+
---------------------
Daniel is 42
Kathryn is 14
---------------------
check:
(2) +d+-+7+=+5%2A%28+k+-+7+%29+
(2) +42+-+7+=+5%2A%28+14+-+7+%29+
(2) +35+=+5%2A7+
(2) +35+=+35+
OK

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
. Please help me solve this equation:Daniel is three times as old as kathryn. seven years ago, daniel was five times as old as kathryn. How are old they?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

D = 3K            (1)     (Daniel is three times as old as kathryn)
D-7 = 5*(K-7)     (2)     (Seven years ago . . . )

Substitute the expression (1) for D into (3).

Then solve the single equation for K.

It is how all (almost all) age problems are solved.

See the lessons
    - Age problems and their solutions
    - A fresh formulation of a traditional age problem
    - Really intricate age word problem
    - Selected age word problems from the archive
    - Age problem for the day of April, 1
in this site.