Question

The Bangor Coat Factory found that the number of coats sold N varies directly as their advertising budget A and inversely as the price of each coat P. The Bangor Coat Factory sold 10,800 coats when $30,000 was spent on advertising and the price of a coat was set at $50. Determine the number of coats sold when the amount spent on advertising is increased to $70,000. HELP PLEASE

Answer 1

Help please i am studying for my final exam

Answer 2

Are you familiar with direct and inverse variation?

Answer 3

Or is it the word problem format that is giving you trouble... or maybe both? :)

Answer 4

its both

Answer 5

OK, let me give you some basic definitions:
If Y varies directly with X, then \[Y = cX.\]
If Y varies inversely with X, then \[Y = c\left(\frac{1}{X} \right).\]
If Y varies directly with A, but inversely with B at the same time, then \[Y = c \left(\frac{A}{B} \right).\]
In all of these, c is some unknown number or constant to be determined based on the information given.

Answer 6

The situation we have is the third one (both directly and inversely). Let me know if that makes sense and if you have any questions. :) Once you are satisfied, we can continue.

Answer 7

ok so how would i set up the equation i have a hard time translating story problems into equations

Answer 8

Alright, so N varies directly with A and inversely with P. This means we use the third definition to get:
\[N = c \left(\frac{A}{P} \right)\]
which is the equation we will work with during the problem.

Answer 9

Basically, "directly" means put the thing on top of a fraction, while "inversely" means put it in the bottom of the fraction.

Answer 10

We've now translated the first sentence... any questions so far? :)

Answer 11

nope

Answer 12

Alright, so now for that second sentence...
"10,800 coats when $30,000 was spent on advertising and the price of a coat was set at $50"
Have no idea what all that means, but let's translate.

From the first sentence we know that N is the number of coats, A is the advertising, and P is the price.

So, our equation now looks like

N = c(A/P)
10,800 = c(30,000/50)

Make sense so far? We still don't know what c is yet.

Answer 13

Yah that makes sense ok so how do we figure out c

Answer 14

Alright, so now, we solve the equation:
10,800 = c*600
18 = c.

Answer 15

Now that c is solved, this is the same for all future uses of the equation we came up with. What I mean is:
N = 18*(A/P)
forever in this problem now.

Answer 16

Only one more sentence left... hang in there. :) Any questions?

Answer 17

nope

Answer 18

Alright then, here we go!

Answer 19

We want to figure out how many coats there will be if we change A to 70,000. I guess we are supposed to keep P the same at 50, since they didn't say anything else about it.

So, N = 18*(70,000/50)
N = 18*1400
N = 25,200

We are done! YAY! :)

Answer 20

thank you so much this was one of the few i had issues with on my exam review the last test before i get my diploma

Answer 21

You are welcome! Good luck on your test! :)

Answer 22

thanks