Algebra Pre-Algebra and Basic Algebra Math Forum

May 8th, 2014, 03:22 PM   #1
Newbie

Joined: May 2014
From: USA

Posts: 7
Thanks: 1

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$per pump. This was on hw and this solution received only 5/6 points. What is missing? Quote:  c(x)=x^2-21x+100 x^2-21x+100=28 x^2-21x+100-28=0 x^2-21+72=0 (x-24)(x+3)=0 x-24=0 x=24 x+3=0 x=-3 answer 24 pumps. What is missing? Last edited by skipjack; May 9th, 2014 at 04:45 PM.  May 8th, 2014, 03:38 PM #2 Global Moderator Joined: May 2007 Posts: 6,581 Thanks: 610 (x-24)(x+3)=x^2 -21x - 72, so you got the wrong answer. Last edited by mathman; May 8th, 2014 at 03:38 PM. Reason: typo  May 8th, 2014, 05:01 PM #3 Newbie Joined: May 2014 From: USA Posts: 7 Thanks: 1 edit: So you can't factor it? Please some help or hint how to solve it. Last edited by MathQuestion; May 8th, 2014 at 05:05 PM. May 8th, 2014, 06:54 PM #4 Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,102 Thanks: 906 Quote:  Originally Posted by MathQuestion edit: So you can't factor it? Please some help or hint how to solve it. Solve WHAT? 1,20 : 80 ...if x = 1 or 20, avg. cost = 80 ; similarly down the line! 2,19 : 62 3,18 : 46 4,17 : 32 5,16 : 20 6,15 : 10 7,14 : 2 8,13 : -4 9,12 : -8 10,11: -10 Looks like "what's missing" is a sensible function May 8th, 2014, 07:21 PM #5 Newbie Joined: May 2014 From: USA Posts: 7 Thanks: 1 Quote:  Originally Posted by Denis Solve WHAT? 1,20 : 80 ...if x = 1 or 20, avg. cost = 80 ; similarly down the line! 2,19 : 62 3,18 : 46 4,17 : 32 5,16 : 20 6,15 : 10 7,14 : 2 8,13 : -4 9,12 : -8 10,11: -10 Looks like "what's missing" is a sensible function Thanks for trying to help Dennis. Solve what is asked in the problem, can you please read it? "Determine the number of pumps that the company needs to produce in order to have an average cost of 28$ per pump"

Last edited by skipjack; May 9th, 2014 at 01:28 PM.

 May 8th, 2014, 07:25 PM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,102 Thanks: 906
May 8th, 2014, 07:42 PM   #7
Newbie

Joined: May 2014
From: USA

Posts: 7
Thanks: 1

Quote:
 Originally Posted by Denis
Thanks. Just one more thing. It has to have two solutions because it is quadratic equation, correct?

May 8th, 2014, 08:05 PM   #8
Math Team

Joined: Oct 2011

Posts: 13,102
Thanks: 906

Quote:
 Originally Posted by MathQuestion 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?

May 8th, 2014, 08:14 PM   #9
Newbie

Joined: May 2014
From: USA

Posts: 7
Thanks: 1

Quote:
 Originally Posted by Denis 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 01:34 PM. Reason: to add parentheses

May 8th, 2014, 08:37 PM   #10
Math Team

Joined: Oct 2011

Posts: 13,102
Thanks: 906

Quote:
 Originally Posted by MathQuestion 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"

 Tags completely, completly, solve

 Thread Tools Display Modes Linear Mode

 Contact - Home - Forums - Cryptocurrency Forum - Top