You are the onwer of a bird store, and you use them to organize your cages. If you keep 1 bird per cage, there will be one bird outside of the cage, therefore it will be missing cages. If you keep two birds per cage, there will be one empty cage. How many birds and cages do you have?

Question

asnaseer · Answer

easiest way to solve this is to convert the word statements into algebra

asnaseer · Answer

start by letting
b=number of birds
c = number of cages

can you convert this sentence into an algebraic expression using "b" and "c"?
"If you keep 1 bird per cage, there will be one bird outside of the cage"

asnaseer · Answer

so how many more birds do we have than cages?

anonymous · Answer

idk im soo confused

asnaseer · Answer

it is not that difficult - read what it is telling you carefully

anonymous · Answer

why wont u tell me lol. i have been trying to figure this out for 2 hours

asnaseer · Answer

The aim of this site is to teach - not just to give answers out.

If you are willing to learn then I will help you.

anonymous · Answer

so whats step one

asnaseer · Answer

what does this sentence tell you about the number of birds compared to the number of cages?

"If you keep 1 bird per cage, there will be one bird outside of the cage"

anonymous · Answer

every bird in cage u have you have a bird out of a cage?

asnaseer · Answer

not quite, I believe the sentence woud be better worded like this:

"If you keep 1 bird per cage, then there will be one bird left with no cage to put in to"

anonymous · Answer

so 1 bird 2 cages?

asnaseer · Answer

no - remember we started by saying there are "b" birds and "c" cages.

now, if each cage has 1 bird placed in it, then there will be one bird left over.

so how many more birds do we have than cages?

anonymous · Answer

1

asnaseer · Answer

correct, so we can write this as:$$b=c+1$$where "b" is the number of birds and "c" is the number of cages.

agreed?

anonymous · Answer

yea

asnaseer · Answer

now look at this sentence:

"If you keep two birds per cage, there will be one empty cage"

now, if you keep 2 birds in each cage, then how many birds will there be in each of the following:

a) 2 cages?
b) 5 cages?
c) 10 cages?

asnaseer · Answer

i.e.:

a) 2 cages hold ? birds
b) 5 cages hold ? birds
c) 10 cages hold ? birds

can you fill-in the question marks?

anonymous · Answer

a) 4. b) 10 C) 20

asnaseer · Answer

perfect! so you would agree that if we divide the number of birds by 2, then we will get how many cages they have been placed in?

asnaseer · Answer

since we are told that there are 2 birds in each cage

anonymous · Answer

ok

asnaseer · Answer

now look at this sentence again:

"If you keep two birds per cage, there will be one empty cage"

with 2 birds per cage, we know that the number of cages that they have been placed in must be b/2, and we are told that there will be one empty cage left over. therefore b/2 must equal one less than the total number of cages, i.e.:$$\frac{b}{2}=c-1$$agreed?

anonymous · Answer

yea

asnaseer · Answer

now multiply this equation by 2 on both sides and what do you get?

anonymous · Answer

what equation?

asnaseer · Answer

the one I just wrote down up there with b/2 = c - 1 ^^^

anonymous · Answer

3

asnaseer · Answer

????

asnaseer · Answer

$$2\times\frac{b}{2}=2\times(c-1)$$simplify this equation

anonymous · Answer

-1

asnaseer · Answer

I'm afraid I am going to have to leave this, it seems like you first need to learn about basic algebra before attempting a question like this. You may find this site useful: http://www.mathsisfun.com/algebra/ Try this question again after you have brushed up on your algebra. Good luck...

anonymous · Answer

o w8 its 0