Difficult Math Problem #89 - Algebra

[800guy]

A clothing manufacturer has determined that she can sell 100 suits a week at a selling price of 200$ each. For each rise of 4$ in the selling price she will sell 2 less suits a week. If she sells the suits for x$ each, how many dollars a week will she receive from sales of the suits?

[g2000]

According to your description...Quantity for sale
100 200
98 204
96 206
To me, it is similar to a demand curve, namely a down slope graph. Next find the equation of this graph.

(y - 100) / (x - 200) = (100 - 98 ) / (200 - 204)
2y - 200 = - (x - 200)
y = - x / 2 + 200
This is just the graph that shows the numerical relationship between quantity for sale and the price.

We have to find the dollars she receives from sale. It is the product of the numbers or the area of the graph.

Area = y * x
x * (-x / 2 + 200)
x * (200 - x/2) (ans)

[maxim730]

is it me or all the fonts showing up incorrectly?

this is what i see:

"According to your description... #ed_op#br#ed_cl#Quantity for sale             $#ed_op#br#ed_cl#   "

[beatthegmat]

Hi maxim730:

It's not just you--the last fifty or so posts are screwed up because of a poor implementation of a text editor I tried yesterday.

I've restored our old editor, and later today I will be manually editing the last fifty posts made to clean up the gibberish.

Thanks for your patience, we're back in business!

[800guy]

OA:

Let y be the number of $4 increases she makes, and let S be the number of suits she sells. Then
X = 200 + 4y ==> y = x/4 - 50
S = 100 - 2y ==> S = 100 - 2[x/4 - 50] = 100 - x/2 + 100 = 200 - x/2

so the answer is that the number of suits she'll sell is 200 - x/2

[ashish1354]

can someone suggest a simpler solution to this problem??

[stop@800]

Lets assume 4$ price increase is 1 unit increase

Price: x [assumed tobe > 200]

extra price = x-200
units increase = (x-200)/4

for each unit increase no of items decreases by 2
so total decrease in no of items = 2 * (x-200) / 4

The no of items will now be = 100 - "total decrease in no of items"

= 100 - 2 * (x-200) / 4

Price = no of items * price per item [price here is = x and no of items we just calculated]

Price = [ 100 - 2 * (x-200) / 4 ] *x

Simplify and you will have your answer.

No look at the equation and try to derive it directly from calculation.
You actually do not need this much written work.
This is the reason, I have not simplified the equation.