SOLUTION: Trudy went to the arcade at the state fair to win some goldfish. she already had some at home, but she wanted more. Right away, trudy won enough goldfish to double her stock. howev

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Question 755394: Trudy went to the arcade at the state fair to win some goldfish. she already had some at home, but she wanted more. Right away, trudy won enough goldfish to double her stock. however, her mom made her give four to her cousin. she put her new ones in the fish tank with the others, but the next morning, half of her goldfish had died. trudys friend kim gave her six more. unfortunetly the next morning two-thirds of her goldfish had died. trudy gave one to her neighbor and then she was left with 2. how many goldfish did trudy start with?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the number of goldfish she
has at home
After winning some at the fair she then has
+2x+ goldfish
After giving +4+ to her cousin, she has
+2x+-+4+
Half of her fish died, so now she has
+%28+2x+-+4+%29+%2F+2+ goldfish
Trudy's friend kim gave her six more, so then she has
++%28+2x+-+4+%29+%2F+2+%2B+6+ goldfish
The next morning two-thirds of her goldfish had died, so she has
+%281%2F3%29%2A%28+%28+2x+-+4+%29+%2F+2+%2B+6+%29+ left
She gave one to her neighbor, so then she has
+%281%2F3%29%2A%28+%28+2x+-+4+%29+%2F+2+%2B+6+%29+-+1+
She has 2 goldfish left, so
+%281%2F3%29%2A%28+%28+2x+-+4+%29+%2F+2+%2B+6+%29+-+1+=+2+
Multiply both sides by +3+
++%28+2x+-+4+%29+%2F+2+%2B+6++-+3+=+6+
++%28+2x+-+4+%29+%2F+2+=+3+
Multiply both sides by +2+
+2x+-+4+=+6+
+2x+=+10+
+x+=+5+
Trudy started with 5 goldfish at home
--------------
After the arcade, she has 10
After giving 4 to her cousin, she has 6
After half died, she has 3
After her friend gives her 6, she has 9
After 2/3 of them die, she has 1/3 or 3 left
She gave 1 to her neighbor and has 2 left
OK