MHB How many birds are at the top and bottom of the tree?

[mathdad]

Some birds are at the top of the tree while the others are at the botton, if one bird goes up, the birds of the top of the tree will be twice as the below of the tree while if one bird comes down the number of the birds at the top of the tree and below will be the same. How many birds are at the top and below of the tree?

 

[tkhunny]

[TIKZ][/TIKZ]

Some birds are at the top of the tree while the others are at the botton, if one bird goes up, the birds of the top of the tree will be twice as the below of the tree while if one bird comes down the number of the birds at the top of the tree and below will be thesame. How many birds are at the top and below of the tree?

I'll do most of it for you. You show us the rest.

T = # of birds at the Top of the Tree
B = # of birds at the Bottom of the Tree

Okay, you're almost done! Go!

 

[mathdad]

[TIKZ][/TIKZ]

I'll do most of it for you. You show us the rest.

T = # of birds at the Top of the Tree
B = # of birds at the Bottom of the Tree

Okay, you're almost done! Go!

T = birds on top of tree

B = birds at the base of the tree

T = 2B
T - 1 = B

2B - 1 = B

2B - B = 1

B = 1

T = 2(1) or 2

Wrong, of course.

 

[MarkFL]

"Some birds are at the top of the tree while the others are at the bottom"

T = # of birds at the top
B = # of birds st the bottom

"if one bird goes up, the birds of the top of the tree will be twice as the below of the tree"

T + 1 = 2(B - 1)

"if one bird comes down the number of the birds at the top of the tree and below will be the same"

T - 1 = B + 1

What do you get when you solve the system?

 

[tkhunny]

Wrong, of course.

We WILL have to work on that attitude. Take a deep breath. You CAN do it.

 

[mathdad]

"Some birds are at the top of the tree while the others are at the bottom"

T = # of birds at the top
B = # of birds st the bottom

"if one bird goes up, the birds of the top of the tree will be twice as the below of the tree"

T + 1 = 2(B - 1)

"if one bird comes down the number of the birds at the top of the tree and below will be the same"

T - 1 = B + 1

What do you get when you solve the system?

Very good. I can take it from here.

 

[mathdad]

"Some birds are at the top of the tree while the others are at the bottom"

T = # of birds at the top
B = # of birds st the bottom

"if one bird goes up, the birds of the top of the tree will be twice as the below of the tree"

T + 1 = 2(B - 1)

"if one bird comes down the number of the birds at the top of the tree and below will be the same"

T - 1 = B + 1

What do you get when you solve the system?

T = birds currently at top
B = birds currently at bottom

2(B-1) = T+1
T-1 = B+1
T = B +2
2B -2 = B +2 +1
B = 5
T = 7