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?
5 answers
originally it had 2997
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!
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!
kajdhkajhdd
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
33
37
310
325
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.
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.