SOLUTION: Steve is three and half times as old as robert. In 8 years, Roberts age will be one half that of Steve. What are their present ages?

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Question 1136866: Steve is three and half times as old as robert. In 8 years, Roberts age will be one half that of Steve. What are their present ages?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Steve's age now
Let +b+ = Robert's age now
------------------------------------
(1) +a+=+%28+7%2F2+%29%2Ab+
(2) +b+%2B+8+=+%281%2F2%29%2A%28+a+%2B+8+%29+
-------------------------------------
(1) +b+=+%282%2F7%29%2Aa+
Plug (1) into (2)
(2) +%282%2F7%29%2Aa+%2B+8+=+%281%2F2%29%2A%28+a+%2B+8+%29+
Multiply both sides by +14+
(2) +4a+%2B+112+=+7a+%2B+56+
(2) +3a+=+56+
(2) +a+=+18+%2B+2%2F3+
and
(1) +b+=+%282%2F7%29%2A%2856%2F3%29+
(1) +b+=+16%2F3+
(1) +b+=+5+%2B+1%2F3+
-------------------------------
Steve is 18 and 8 months
Robert is 5 and 4 months
-------------------------------
check:
(2) +16%2F3+%2B+8+=+%281%2F2%29%2A%28+56%2F3+%2B+8+%29+
(2) +16%2F3+%2B+8+=+28%2F3+%2B+4+
(2) +16+%2B+24+=+28+%2B+12+
(2) +40+=+40+
OK
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