SOLUTION: Sam and Anna together had $100. After giving Anna $10.00, Sam finds that he has $4.00 more that 1/5 the amount Anna now has. How much does Sam now have?

Algebra ->  Finance -> SOLUTION: Sam and Anna together had $100. After giving Anna $10.00, Sam finds that he has $4.00 more that 1/5 the amount Anna now has. How much does Sam now have?      Log On


   

Question 885434: Sam and Anna together had $100. After giving Anna $10.00, Sam finds that he has $4.00 more that 1/5 the amount Anna now has. How much does Sam now have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Sam and Anna together had $100
Let +x+ = the amount that Sam had
+100+-+x+ is the amount that Anna had
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He gives Anna $10, so Anna has
+100+-+x+%2B+10+ and Sam has
+x+-+10+
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given:
+x+-+10+=+%28+1%2F5%29%2A%28+100+-+x+%2B+10+%29+%2B+4+
Multiply both sides by +5+
+5%2A%28+x+-+10+%29+=+100+-+x+%2B+10+%2B+20+
+5x+-+50+=+130+-+x+
+6x+=+180+
+x+=+30+
and
+x+-+10+=+20+
Sam now has $20
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check:
Sam had $30
Anna Had $70
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He gave $10 to Anna, so
Sam has $20
Anna has $80
+x+-+10+=+%28+1%2F5%29%2A%28+100+-+x+%2B+10+%29+%2B+4+
+20+=+%28+1%2F5%29%2A%28+70+%2B+10+%29+%2B+4+
+100+=+80+%2B+20+
+100+=+100+
OK