SOLUTION: Last year, Sam was 10 year-old younger than Richard. This year, the age of Sam is three-fifth of that of Richard. How old is Sam this year?

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Question 1105080: Last year, Sam was 10 year-old younger than Richard. This year, the age of Sam is three-fifth of that of Richard. How old is Sam this year?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Sam's age now
Let +b+ = Richard's age now
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(1) +a+-+1+=+%28+b+-+1+%29+-+10+
(2) +a+=+%283%2F5%29%2Ab+
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(1) +a+-+1+=+b+-+11+
(1) +a+=+b+-+10+
Plug (2) into (1)
(1) +%283%2F5%29%2Ab++=+b+-+10+
(1) +%282%2F5%29%2Ab+=+10+
(1) +b+=+%285%2F2%29%2A10+
(1) +b+=+25+
and
(2) +a+=+%283%2F5%29%2A25+
(2) +a+=+15+
Sam is 15 this year
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check answer:
(1) +a+=+b+-+10+
(1) +15+=+25+-+10+
(1) +15+=+15+
and
(2) +a+=+%283%2F5%29%2Ab+
(2) +15+=+%283%2F5%29%2A25+
(2) +15+=+15+
OK