Question

The number of cars (c) in a parking lot increases when the parking fee (f) decreases. Write the correct equation for this scenario, and solve for the number of cars when the fee is $6.


Fee Cars
20 15
30 10

c = − 300 over f

c = 300 over f

c = 3f; c = 18

c = 3f; c = 2

Can anyone please guide me through this question? @johnweldon1993 @ajprincess @phi @Opcode @Gabylovesyou @anonymous_user @DLS

Answer 1

@myininaya @Compassionate

Answer 2

@zepdrix can u plz help out?

Answer 3

@KlOwNlOvE @MrNood @midhun.madhu1987

Answer 4

can anyone just help me understand what I need to do? i need help!

Answer 5

Well lets see...when 1 function increases, the other decreases...that reminds me of an inverse variation...or

\[\large c = \frac{k}{f}\]

As that function shows, as F gets bigger, C gets smaller...but what we want (and have) is that as F (the fee) gets smaller) the cars (C) gets bigger.

So now...we need to be able to solve for that 'k' there....so lets choose a point we have from that little table there

Answer 6

when there are 10 cars...the fee was 30 dollars...so

\[\large c = \frac{k}{f}\]
\[\large 10 = \frac{k}{30}\]
\[\large k = 300\]

so there will be a constant of variation of 300....so our new quation that we will want to use to solve our problem will be

\[\large c = \frac{300}{f}\]

Answer 7

But just to be sure...lets check the second point we have on the table

15 cars at a fee of 20 dollars.

so

\[\large 15 = \frac{300}{20}\]
\[\large 300 = 300\]

so yes it checks out...

Answer 8

Now, we are to solve how many cars there will be when the fee (f) is 6 dollars...so we plug in 6 for 'f' in our equation and solve for 'c'

\[\large c = \frac{300}{6}\]
\[\large c = ?\]

Answer 9

c= 50

Answer 10

Perfect...there will be 50 cars when the fee is just 6 dollars

Answer 11

OOOOOHHH! okaay but why did we choose the second one we couldve plugged in 6 for f on the other choices and get a random answer @johnweldon1993

Answer 12

Not sure what you mean...

Answer 13

can u explain to me why it had to be choice B out of all the choices? sorry i'm confused myself lol

Answer 14

@johnweldon1993

Answer 15

But we just solved for why it would be choice B

Note that with the little table we were given, we can just take the values given and plug them in to check if we didnt want to do all the work

so for example with the

15 cars at a fee of 20 dollars...

if we plug that into the first choice we would have

\[\large 15 = \frac{-300}{20}\]
\[\large 300 \cancel{=}-300\] so that choice wouldnt have worked

and do it again with the other choices etc... easy way to guess and check instead of doing the work above

Answer 16

OHHHHH okayyy noooww i get itt!! thanks soo much!

Answer 17

Anytime :)

Answer 18

why did u use 15 and 20 when they say that fees is 6?

Answer 19

i'm slow in math LOL

Answer 20

So can is B the answer?

Answer 21

@johnweldon1993