SOLUTION: Jane brought some muffins for $4. She ate three herself, and resold the rest at a profit of 20 cents per muffin. If Jane sold the muffins for a total of $3.50, how much did she cha

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Jane brought some muffins for $4. She ate three herself, and resold the rest at a profit of 20 cents per muffin. If Jane sold the muffins for a total of $3.50, how much did she cha      Log On

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Question 879352: Jane brought some muffins for $4. She ate three herself, and resold the rest at a profit of 20 cents per muffin. If Jane sold the muffins for a total of $3.50, how much did she charge for each muffin?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of muffins she started with
+4%2Fn+ = the cost per muffin
+%284%2Fn%29%2A3+=+12%2Fn+ = the cost of 3 muffins
+n+-+3+ = the number of muffins she resold
+%28+4+-+12%2Fn+%29%2F%28+n-3+%29+ = the cost per muffin that she resold
+3.5+%2F+%28+n+-+3+%29+ = her resale price per muffin
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She resold +n-3+ muffins at +.2+ dollars profit per muffin
I can say:
+3.5+%2F+%28+n-3+%29+-+%28+4+-+12%2Fn+%29+%2F+%28+n-3+%29++=+.2+
+3.5+-+%28+4+-+12%2Fn+%29+=+.2%2A%28+n-3+%29+
+3.5+-+4+%2B+12%2Fn+=+.2n+-+.6+
+-.5+%2B+.6+=+.2n+-+12%2Fn+
+.1+=+.2n+-+12%2Fn+
+.1n+=+.2n%5E2+-+12+
+.2n%5E2+-+.1n+-+12+=+0+
+2n%5E2+-+n+-+120+=+0+
+n+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+n+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2+-+4%2A2%2A%28-120%29+%29%29%2F%282%2A2%29+
+n+=+%28+1+%2B-+sqrt%28+1+%2B+960+%29%29%2F+4+
+n+=+%28+1+%2B-+sqrt%28+961+%29%29%2F+4+
+n+=+%28+1+%2B+31+%29+%2F+4+
+n+=+32%2F4+
+n+=+8+
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she charged per muffin:
+3.5+%2F+%28+n+-+3+%29+
+3.5+%2F+%28+8+-+3+%29+=+3.5%2F5+
+3.5%2F5+=+.7+
70 cents per muffin
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check:
+8+ = the number of muffins she started with
+4%2F8+=+.5+ = the cost per muffin
+%284%2F8%29%2A3+=+12%2F8+ = the cost of 3 muffins
+8+-+3+=+5+ = the number of muffins she resold
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+%28+4+-+12%2F8+%29%2F%28+8-3+%29+ = the cost per muffin that she resold
+2.5%2F5+=+.5+ = the cost per muffin that she resold
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+3.5+%2F+%28+8+-+3+%29+ = her resale price per muffin
+3.5%2F5+=+.7+ = her resale price per muffin
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Hope I got it!