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May 8th, 2014, 04:22 PM   #1
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Please help solve this completely

Hi there. New member here, I hope someone can help with this problem.

The president of a company producing water pumps has gathered data that suggests that the average cost in dollars of producing x pumps will be
C(x)=x^2-21x+100. Determine the number of pumps that the company needs to produce in order to have an average cost of 28$ per pump.

This was on hw and this solution received only 5/6 points.

What is missing?

Quote:
c(x)=x^2-21x+100

x^2-21x+100=28

x^2-21x+100-28=0

x^2-21+72=0

(x-24)(x+3)=0

x-24=0
x=24

x+3=0
x=-3

answer 24 pumps.
What is missing?

Last edited by skipjack; May 9th, 2014 at 05:45 PM.
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May 8th, 2014, 04:38 PM   #2
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(x-24)(x+3)=x^2 -21x - 72, so you got the wrong answer.

Last edited by mathman; May 8th, 2014 at 04:38 PM. Reason: typo
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May 8th, 2014, 06:01 PM   #3
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edit:
So you can't factor it? Please some help or hint how to solve it.

Last edited by MathQuestion; May 8th, 2014 at 06:05 PM.
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May 8th, 2014, 07:54 PM   #4
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Quote:
Originally Posted by MathQuestion View Post
edit:
So you can't factor it? Please some help or hint how to solve it.
Solve WHAT?
1,20 : 80 ...if x = 1 or 20, avg. cost = 80 ; similarly down the line!
2,19 : 62
3,18 : 46
4,17 : 32
5,16 : 20
6,15 : 10
7,14 : 2
8,13 : -4
9,12 : -8
10,11: -10

Looks like "what's missing" is a sensible function
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May 8th, 2014, 08:21 PM   #5
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Quote:
Originally Posted by Denis View Post
Solve WHAT?
1,20 : 80 ...if x = 1 or 20, avg. cost = 80 ; similarly down the line!
2,19 : 62
3,18 : 46
4,17 : 32
5,16 : 20
6,15 : 10
7,14 : 2
8,13 : -4
9,12 : -8
10,11: -10

Looks like "what's missing" is a sensible function
Thanks for trying to help Dennis. Solve what is asked in the problem, can you please read it?
"Determine the number of pumps that the company needs to produce in order to have an average cost of 28$ per pump"

Last edited by skipjack; May 9th, 2014 at 02:28 PM.
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May 8th, 2014, 08:25 PM   #6
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Was trying to be humorous

Here's a similar one:

SOLUTION: The president of a company producing water pumps has gathered data suggesting that the average cost in dollars of producing x units per hour of a new style of pump will be c(x)=x^2
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May 8th, 2014, 08:42 PM   #7
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Thanks. Just one more thing. It has to have two solutions because it is quadratic equation, correct?
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May 8th, 2014, 09:05 PM   #8
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Quote:
Originally Posted by MathQuestion View Post
Thanks. Just one more thing. It has to have two solutions because it is quadratic equation, correct?
Correct.
x^2 - 21x + 100 = 28x
x^2 - 49x + 100 = 0
Solving using quadratic formula gives x = 47 or 2 (rounded).
Is that what you got?
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May 8th, 2014, 09:14 PM   #9
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Quote:
Originally Posted by Denis View Post
Correct.
x^2 - 21x + 100 = 28x
x^2 - 49x + 100 = 0
Solving using quadratic formula gives x = 47 or 2 (rounded).
Is that what you got?
No, I did it like this.

x^2 - 21x + 100 = 28
x^2 - 21x + 100 - 28 = 0
x^2 - 21x + 72 = 0

x= 21/2 +- V((21/2)^2 -72)

V represents square root.

x= 10.5+-V38.25
x=10.5+-6.1844658438

x1=4.315341562
x2=16.68465844

Last edited by skipjack; May 9th, 2014 at 02:34 PM. Reason: to add parentheses
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May 8th, 2014, 09:37 PM   #10
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Quote:
Originally Posted by MathQuestion View Post
no I did it like this.
x^2 - 21x + 100 = 28
The question is:
"Determine the number of pumps that the company needs to produce
in order to have an average cost to 28$ per pump."
So that translate to:
x^2 - 21x + 100 = 28x ......"28 per pump, the pumps = x"
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