SOLUTION: Penny bought a scarf for $5.00, spent ½ of her remaining money on jogging shoes, bought lunch for $2.00, then spent ½ of the remaining money on a present. She then had $10 left. Ho

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Penny bought a scarf for $5.00, spent ½ of her remaining money on jogging shoes, bought lunch for $2.00, then spent ½ of the remaining money on a present. She then had $10 left. Ho      Log On

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Question 751273: Penny bought a scarf for $5.00, spent ½ of her remaining money on jogging shoes, bought lunch for $2.00, then spent ½ of the remaining money on a present. She then had $10 left. How much money did she start with?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = amount of money she started with
After buying scarf for $5, she has +x+-+5+ remaining
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She spent ½ of her remaining money on jogging shoes, or
+%28+x-5+%29+%2F+2+, and she has +%28+x-5+%29%2F+2+ left.
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She bought lunch for $2.00
She has +%28+x-5+%29+%2F2+-+2+ left
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She spent ½ of the remaining money on a present, so
she has +%28%28%28+x-5+%29+%2F2+-+2+%29%29+%2F+2+ left
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She has $10 left, so
+%28%28%28+x-5+%29+%2F2+-+2+%29%29+%2F+2+=+10+
+%28+x-5+%29+%2F2+-+2++=+20+
+%28+x-5+%29+%2F+2+=+22+
+x+-+5+=+44+
+x+=+49+
She started with $49
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check:
After buying scarf for $5, she has $44 remaining
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She spent ½ of her remaining money on jogging shoes, or
$22, and she has $22 left.
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She bought lunch for $2.00
She has $20 left
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She spent ½ of the remaining money on a present, so
she has $10 left
OK