SOLUTION: The sum of my age and my daughter's is 50 years. In 30 years, 3 times my age increased by my daughter's age will be equal to 242 years. How old are we today?

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Question 573418: The sum of my age and my daughter's is 50 years. In 30 years, 3 times my age increased by my daughter's age will be equal to 242 years. How old are we today?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +f+ = Father's age now
Let +d+ = Daughter's age now
+f+%2B+30+ = father's age 30 yrs from now
+d+%2B+30+ = Daughter's age 30 yrs from now
----------
given:
(1) +f+%2B+d+=+50+
(2) +3%2A%28+f+%2B+30+%29+%2B+d+%2B+30+=+242+
------------------
(1) +d+=+50+-+f+
Substitute (1) into (2)
(2) +3%2A%28+f+%2B+30+%29+%2B+50+-+f+%2B+30+=+242+
(2) +3f+%2B+90+-+f+%2B+80+=+242+
(2) +2f+=+242+-+170+
(2) +2f+=+72+
(2) +f+=+36+
and, since
(1) +d+=+50+-+f+
(1) +d+=+50+-+36+
(1) +d+=+14+
I am 36 and my Daughter is 14
check:
(2) +3%2A%28+f+%2B+30+%29+%2B+d+%2B+30+=+242+
(2) +3%2A%28+36+%2B+30+%29+%2B+14+%2B+30+=+242+
(2) +3%2A66+%2B+44+=+242+
(2) +198+%2B+44+=+242+
(2) +242+=+242+
OK