SOLUTION: Author is 10 years older than Carol. 9 years ago his age was 3 times her age. How old will they each be in 4 years?

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Question 697611: Author is 10 years older than Carol. 9 years ago his age was 3 times her age. How old will they each be in 4 years?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Arthur's age now
Let +b+ = Carol's age now
given:
(1) +a+=+b+%2B+10+
(2) +a+-+9+=+3%2A%28+b+-+9+%29+
-----------------------
(2) +a+-+9+=+3b+-+27+
(2) +a+-+3b+=+-18+
and
(1) +a+-+b+=+10+
------------------
Subtract (2) from (1)
(1) +a+-+b+=+10+
(2) +-a+%2B+3b+=+18+
+2b+=+28+
+b+=+14+
and
(1) +a+=+b+%2B+10+
(1) +a+=+14+%2B+10+
(1) +a+=+24+
--------------
+a+%2B+4+=+28+
+b+%2B+4+=+18+
In 4 years Arthur will be 24
In 4 years Carol will be 18
----------------------
check:
(2) +a+-+9+=+3%2A%28+b+-+9+%29+
(2) +24+-+9+=+3%2A%28+14+-+9+%29+
(2) +15+=+3%2A5+
(2) +15+=+15+
OK