Question

The number of birds (b) in a park increases when the number of dogs in the park (d) decreases. Write the correct equation for this scenario and solve for the number of birds when there are 10 dogs.

Dogs Birds
40 10
50 8

b = 4d; b = 40

b = 4d; b = 2.5

b = 400 over d; b= 4000

b = 400 over d b = 40

Answer 1

I think that it is b=4d ; b=40

Since you multiply 4*10=40 and the number of birds increases as the number of dogs decreases.

Answer 2

btw, dogs don't eat birds :P

Answer 3

well, I guess they could, wild dogs would, but domestic ones do not

Answer 4

If they were starving, they would.

Answer 5

so, there's an assumption people go to the park with starving dogs, as opposed to well-fed dogs but just for an outting

Answer 6

so, one amount gets affected by the change in the other
usually called a DIRECT VARIATION, that is to say that one item VARIES DIRECTLY as the other changes
something like say

y = 2x
x = 25
y = 2(25) = 50
x = 100
y = 2(100) = 200
and so on ...

so one can say that
b = (SOME NUMBER) d

what's that number? we dunno
but we know that
------------------------
Dogs Birds
40 10
50 8
-----------------------

so when b = 40, d = 10

so let's plug that in

b = (SOME NUMBER) d
40 = (SOME NUMBER) 10

now just solve for "SOME NUMBER"

Answer 7

hmmm

Answer 8

anyhow, I notice my 1st figure didn't match the 2nd.... so it an inverse one, so lemme rewrite what I said

Answer 9

in your case is pretty much the same much the same thing, just inverse
so called INVERSE VARIATION
that is something VARIES INVERSELY as changes occur to another
it'd be written as \(\bf b = \cfrac{\textit{some number}}{d}\)

same as before, we dunno what the number is
but we know that
------------------------
Dogs Birds
40 10
50 8
-----------------------

when d = 40, b = 10
so \(\bf b = \cfrac{\textit{some number}}{d} \implies 40 = \cfrac{\textit{some number}}{10}\)

solve for "some number"

Answer 10

$$
m={\triangle\text{Birds}\over\triangle\text{Dogs}}={8-10\over50-40}=\dfrac{-1}{5}\\
B(D)={-1\over5}D+B_i\text{, where }B_i\text{ is the number of Birds where there are no Dogs. }\\
B(40)=10={-1\over5}(40)+B_i\implies B_i=18\\
\text{So, }B(D)={-1\over5}D+18\text{.}\\
B(10)={-1\over5}(10)+18=40.\\
\text{There would be 40 Birds when there are 10 Dogs.}
$$

Answer 11

Thanks for the help guys!

And @jdoe0001, I wasn't insinuating that a healthy, well fed dog would eat a bird. I meant a homeless dog with no food.

Answer 12

@jdoe0001 So would the last one be the answer?

Answer 13

hmm what do you mean? for the slope exercise?

Answer 14

Never mind I figured it out. Thank you though :) @jdoe0001

Answer 15

did you ever think that the dogs would bark at the birds, lmao you guys go straight to killings lol

Answer 16

ikr