13.50 = 18 - 0.5 sqrt (x - 4) ? (modelling weekly demand)

J

jlaw

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Hello Online Teachers,

Would someone kindly help me with this college algebra course problem? I'm not sure where to start or how to end.

Problem: The owner of a health food store determines that the demand equation for selling a nutritional supplement is p= 18 - 0.5 sqrt (x-4) where p is the price in dollars and x is the number of bottles demanded per week. How many bottles are demanded per week if the price of the supplement is $13.50?

Best I can do so far is:

13.50 = 18 - 0.5 sqrt (x-4)
4.50 = -0.5 sqrt (x-4)
4.50 = -0.25 sqrt (x-4)^2 (x-4)^2

Now I'm stuck. Would I multiply -0.25 with both (x-4)^2 or did I flub up all of it? :?
How do I know which term to move first and from which side to start first or next?

Gratitudes for your sharing your time and knowledge,
Julia
 
Re: 13.50=18 -0.5 sqrt (x-4) ?

You wandered off right away.

13.50 - 18.00 = -4.50 -- That's negative.

-4.50 = -0.5 sqrt (x-4)

Divide by -0.5 (or multiply by -2)

9 = sqrt(x-4)

Square both sides

81 = x-4
 
Thanks for the reply tkhunny. :D

Would I then divide - 4 into 81 to solve for x?
 
jlaw said:
Would I then divide - 4 into 81 to solve for x?
Click to expand...
Erm... Okay, so you need to learn how to work with negative numbers and how to solve linear equations, for a start. (The rest that you were shown is actually more advanced than these topics, and should probably wait until later.) :shock:

Unfortunately, we cannot teach the necessary hours of course instruction, so kindly please consider studying some of the many great lessons available online. :idea:

. . . . .Google results for "negative numbers"

. . . . .Google results for "solving linear equations"

This should get you far enough that you can at least understand some of what's been done for you so far. Please reply, showing your work and reasoning, so we can "see" how you're doing at that point.

Thank you! :D

Eliz.
 
Hi Eliz,
Sorry for the delay. Work was turned in Sunday and I was hoping to receive the class instructor's response before responding back. Academics, college, books and puzzles usually come easy for me but this algebra is a whole other beast and my weakest subject. My degree is set for an Education Certification with an emphasis in English. Algebra is the only subject that completely crushes confidence in my abilities to retain and use information learned. On top of it, it appears that online instructors have a difference of opinions on how certain problems should be solved, causing the confusion to deepen. The below work seemed to make sense but what do I know :oops: ..., cause sincerely, I'm still crawling around looking for a light switch on the "floor". :? Thus, giving me all the more reason to be grateful for everyone's help and time.

"Please reply, showing your work and reasoning, so we can "see" how you're doing at that point." - Eliz.

How's this...
13.50 = 18 - 0.5 sqrt (x-4)
13.50 - 18 = 18 - 18 - 0.5 sqrt (x-4)
(-4.5)^2 = (-0.5 sqrt (x-4))^2
(-4.5)(-4.5) = (-0.5) (0.5) (sqrt (x-4)) (sqrt (x-4))
20.25 = 0.25 (x-4)
20.25 = 0.25x-1
20.25 + 1 = 0.25x - 1 + 1
21.25 = 0.25x

21.25 = x
0.25

85 = x
 
13.50 = 18 - 0.5 sqrt(x - 4)
You can make it simpler (and easier) this way:
Multiply by 2 to get rid of decimals:
27 = 36 - sqrt(x - 4)
re-arrange:
sqrt(x - 4) = 9
square both sides:
x - 4 = 81 ; x = 85
 
Thanks so much for your help Denis, Galactus, Stapel, and TKHunny! :)
 
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