isobel is producing and selling cassette tapes of her rock band. When she had so

Question

isobel is producing and selling cassette tapes of her rock band. When she had sold 10 tapes, her net profit was $6. When she had sold 20 tapes, however, her net profit had shrunk to $5 due to increased production expenses. But when she had sold 30 tapes, her net profit had rebounded to $16. cassetto S, her nepr tsobers net profit y to y=1 200 (b) Divide the profit function in part (a) by the number of tapes sold x to get a model relating average profit w per tape to the number of tapes sold. (c) How many tapes must she sell in order to make $3.71 per tape in net profit? (Enter your answers as a comma-separated list. Round your answers to the nearest whole number.) umber) tapes Additional Materials Reading

Explanation / Answer

10 tapes, profit = 6
20 tapes, profit = 5
30 tapes, profit = 16

So, we have
y = ax^2 + bx + c

Using (10,6) , (20,5) and (30,16) :
6 = 100a + 10b + c
5 = 400a + 20b + c
16 = 900a + 30b + c

Subtracting :
300a + 10b = -1
500a + 10b = 11

Now, subtractin' again :
200a = 12
a = 12/200
a = 0.06

With that, 300*0.06) + 10b = -1
18 + 10b = -1
b = -1.9

And using 6 = 100a + 10b + c ,
6 = 6 - 19 + c
c = 19

So, equation is :
0.06x^2 - 1.9x + 19 ---> ANSWER

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Avg profit :
(0.06x^2 - 1.9x + 19)/x

0.06x + 19/x - 1.9 ----> ANS

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3.71 = (0.06x^2 - 1.9x + 19)/x

Crossmultiplying :
3.71x = 0.06x^2- 1.9x + 19

0.06x^2 - 5.61x + 19 = 0

Solving by quadratic formula :
(5.61 +/- sqrt(31.4721 - 4*0.06*19)) / (2*0.06)

(5.61 +/- 5.1876873460145996) / 0.12

90 or 4 tapes

4,90 ----> ANS

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