SOLUTION: Natalie has some nickles. Dirk has some dimes, and Quincy has some quarters. Dirk has five more dimes than Quincy has quarters. If Natalie gives Dirk a nickel, Dirk gives Quincy a

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: Natalie has some nickles. Dirk has some dimes, and Quincy has some quarters. Dirk has five more dimes than Quincy has quarters. If Natalie gives Dirk a nickel, Dirk gives Quincy a       Log On

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Question 1124778: Natalie has some nickles. Dirk has some dimes, and Quincy has some quarters. Dirk has five more dimes than Quincy has quarters. If Natalie gives Dirk a nickel, Dirk gives Quincy a dime, and Quincy gives Natalie a quarter, they will all have the same amount of money. How much coins did each have originally. Use ONLY ONE variable.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the number of quarters Quincy has originally
+x+%2B+5+ = the number of dimes Dirk has originally
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Natalie gives Dirk a nickel. His coins are worth:
+10%2A%28+x%2B5+%29+%2B+5+ cents
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Dirk gives Quincy a dime.
Dirk痴 coins are worth:
+10%2A%28+x%2B5+%29+%2B+5+-+10+
Quincy痴 coins are worth:
+25x+%2B+10+
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Quincy gives Natalie a quarter
His coins are worth:
+25x+%2B+10+-+25+
Natalie:
She lost a nickel and gained a quarter, so
she is plus +20+ cents
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They all have the same amount now
+25x+-+15+ is Quincy痴 amount
+10%2A%28+x%2B5+%29++-+5+ is Dirk痴 amount
They all have the same amount, so
+25x+-+15+=+10%2A%28+x+%2B+5+%29+-+5+
+25x+-+15+=+10x+%2B+50+-+5+
+15x+=+60+
+x+=+4+
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Quincy had +x+=+4+ coins originally
Dirk had ++x%2B5+=+9+ coins originally
Natalie ended up with +25x+-+15+=+85+ cents,
Which is +20+ cents more than she started with
She started with +65+ cents
She had nickels, so she started with
+65%2F5+=+13+ coins originally
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Get a 2nd opinion if needed