SOLUTION: Build the equation for the number of DVDs, n, In terms of their Price, P. One month a store sells dvds for $5 Each and sells 1200 DVDs. The next month they charge $7.50 and sell 8

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Build the equation for the number of DVDs, n, In terms of their Price, P. One month a store sells dvds for $5 Each and sells 1200 DVDs. The next month they charge $7.50 and sell 8      Log On


   

Question 1151880: Build the equation for the number of DVDs, n, In terms of their Price, P.
One month a store sells dvds for $5 Each and sells 1200 DVDs. The next month they charge $7.50 and sell 800 dvds
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Temporarily, I'm going to use x instead of P.
Also, I'll use y in place of n.
At the end I'll do replacements.

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x = price
y = number of DVDs

"One month a store sells dvds for $5 Each and sells 1200 DVDs." means we have the point (x1,y1) = (5, 1200)

"The next month they charge $7.50 and sell 800 dvds" means we have the point (x2,y2) = (7.5, 800)

Calculate the slope
m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29

m+=+%28800+-+1200%29%2F%287.5+-+5%29

m+=+%28-400%29%2F%282.5%29

m+=+-160
The slope tells us that for each price increase of $1, the number of DVDs sold goes down by 160.

Now turn to the point-slope formula. Plug in the given info. Solve for y.
y-y%5B1%5D+=+m%28x+-+x%5B1%5D%29

y-1200+=+-160%28x+-+5%29

y-1200+=+-160%28x%29+-+160%28-5%29

y-1200+=+-160x+%2B+800

y+=+-160x+%2B+800%2B1200

y+=+-160x%2B2000

n+=+-160%2AP%2B2000 Replace x with P, replace y with n.


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Check:

We should plug in a price of P = 5 and get n = 1200
n+=+-160%2AP%2B2000
n+=+-160%2A5%2B2000
n+=+-800%2B2000
n+=+1200
so that works out. Also, plugging in P = 7.5 should lead to n = 800
n+=+-160%2AP%2B2000
n+=+-160%2A7.5%2B2000
n+=+-1200%2B2000
n+=+800
that works as well. We have the proper equation.

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Answer: n+=+-160%2AP%2B2000