A tree is losing its trees. Two thirds fall off in the first week, two thirds of those remaining fall off in the second week, and two thirds off those remaining fall off in the third week. Now there are 37 leaves. How many leaves did the tree have originally?

Answer 1

originally it had 2997

Answer 2

original : x
at end of 1st week we have 1/3 x left
at end of 2nd week we have (1/3)(1/3 x) left = (1/3)^2 x
at end of 3rd week we have (1/3)^3 x left

so (1/27)x = 37
x = 999

So there were 999 leaves

check:
number falling off 1st week = (2/3)(999) = 666
number left = 333
number falling off 2nd week - (2/3)(666) = 222
number left = 333 - 222 = 111
number falling off 3rd week = (2/3)(111) = 74
number left at end of 3rd week = 111 - 74 = 37
All is good!

Answer 3

kajdhkajhdd

Answer 4

There are (35)2 ⋅ 30 leaves on a tree. What is the total number of leaves on the tree? (5 points)

33
37
310
325

Answer 5

After first week remains 1-\frac{2}{3}=\frac{1}{3}1−
3
2
​
=
3
1
​
leaves

After second week remains \frac{1}{3}-\frac{1}{3}\frac{2}{3}=\frac{1}{9}
3
1
​
−
3
1
​

3
2
​
=
9
1
​
leaves

After third week remains \frac{1}{9}-\frac{1}{9}\frac{2}{3}=\frac{1}{27}
9
1
​
−
9
1
​

3
2
​
=
27
1
​
leaves

Let x be the number of the leaves, the tree starts with.

We have: \frac{x}{27}=37
27
x
​
=37

So, the tree starts with x=27*37=999x=27∗37=999 leaves.