SOLUTION: A newspaper has current circulation of 30,000 and charges 65c per paper. For each 10c rise in price past experience indicates circulation will decrease by 2000. x=number of pri

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Question 1045747: A newspaper has current circulation of 30,000 and charges 65c per paper.
For each 10c rise in price past experience indicates circulation will decrease by 2000.
x=number of price increases
price=0.65+0.10x
Find the increase price of the newspaper to obtain an income of $19,350

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +I+ = income from sales of papers
+I+=+%28+30000+-+2000x+%29%2A%28+65+%2B+.1x+%29+
+I+=+2000%2A%28+15+-+x+%29%2A%28+65+%2B+.1x+%29+
+I+=+2000%2A%28+975+-+65x+%2B+1.5x+-+.1x%5E2+%29+
+19350+=+2000%2A%28+975+-+65x+%2B+1.5x+-+.1x%5E2+%29+
+9.675+=+975+-+63.5x+-+.1x%5E2++
+-.1x%5E2+-+63.5x+%2B+965.325+=+0+
+-x%5E2+-+635x+%2B+9653.25+=+0+
----------------------------
Use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-1+
+b+=+-635+
+c+=+9653.25+

+x+=+%28+635+%2B-+sqrt%28+403225+%2B+38613+%29%29%2F%28%28-2%29%29+
+x+=+%28+635+%2B-+sqrt%28+441838+%29%29%2F%28%28-2%29%29+
+x+=+%28+635+-+664.709+%29+%2F+%28-2%29+
+x+=+%28+-29.709+%29+%2F+%28-2%29+
+x+=+14.854+
15 increases in price will give an income of $19,350
-------------------
check:
+I+=+%28+30000+-+2000x+%29%2A%28+65+%2B+.1x+%29+
+I+=+%28+30000+-+2000%2A14.854+%29%2A%28+65+%2B+.1%2A14.854+%29+
+I+=+%28+30000+-+29708+%29%2A%28+65+%2B+1.4854+%29+
+I+=+292%2A66.4854+
+I+=+19413.74+
I'm a little off from actual income. I must have
a math error, but my method is good , I think