SOLUTION: A group of people receives a bill of $240. Two people left without paying. Each of the remaining people had to pay $4 extra. Let x be the number of people originally, find the valu

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Question 1043917: A group of people receives a bill of $240. Two people left without paying. Each of the remaining people had to pay $4 extra. Let x be the number of people originally, find the value of x.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The original cost/person was +240%2Fx+
After 2 people leave, there are +x+-+2+ left
The new cost/person is:
+240%2F%28+x-2+%29+
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I can say:
+240%2F%28+x-2+%29+=+240%2Fx+%2B+4+
Multiply both sides by +x%2A%28+x-2+%29+
+240x+=+240%2A%28+x-2+%29+%2B+4%2Ax%2A%28+x-2+%29+
+240x+=+240x+-+480+%2B+4x%5E2+-+8x+
+4x%5E2+-+8x+-+480+=+0+
+x%5E2+-+2x+-+120+=+0+
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Use quadratic formula
+x+=+%28+-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-120%29+%29%29%2F%282%2A1%29+
+x+=+%28+2+%2B-+sqrt%28+4+%2B+480+%29%29%2F2+
+x+=+%28+2+%2B-+sqrt%28+484+%29%29%2F2+
+x+=+%28+2+%2B+22+%29+%2F+2+
+x+=+12+ ( choose the positive root )
There were 12 people originally
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check answer:
The original cost/person was:
+240%2F12+=+20+
The cost/person after 2 people left:
+240%2F10+=+24+
The cost/person is now $4 more
OK