SOLUTION: Cybthia's donates oranges to a senior home. In week 1 she took 1/10 of the total of her oranges to the senior home; she took 1/9 of the left over oranges in week 2; she took 1/8 of

Question 1077548: Cybthia's donates oranges to a senior home. In week 1 she took 1/10 of the total of her oranges to the senior home; she took 1/9 of the left over oranges in week 2; she took 1/8 of the left over oranges in week 3; she took 1/7 of the left over oranges in week 4 and so on until week 9. In week 9 she took 1/2 of the left over oranges; and she took all 10 left over oranges from the tree in week 10. What was the total number of oranges on the tree at the beginning?
I worked on it and got 100 but I need a formula. I am not sure how to make it a formula. Or a model.
Found 2 solutions by jorel1380, MathTherapy:
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
Let x be the amount of oranges originally on the tree. Then, the equation you are looking for would be:
x(9/10)(8/9)(7/8)(6/7)(5/6)(4/5)(3/4)(2/3)(1/2)-10=0
So:
x(9/10)(8/9)(7/8)(6/7)(5/6)(4/5)(3/4)(2/3)(1/2)=10
.1x=10
x=100
There were 100 oranges originally. ☺☺☺☺
Answer by MathTherapy(10549) (Show Source): You can put this solution on YOUR website!
Cybthia's donates oranges to a senior home. In week 1 she took 1/10 of the total of her oranges to the senior home; she took 1/9 of the left over oranges in week 2; she took 1/8 of the left over oranges in week 3; she took 1/7 of the left over oranges in week 4 and so on until week 9. In week 9 she took 1/2 of the left over oranges; and she took all 10 left over oranges from the tree in week 10. What was the total number of oranges on the tree at the beginning?
I worked on it and got 100 but I need a formula. I am not sure how to make it a formula. Or a model.

1st week: Remainder =
2nd week: Remainder =
3rd week: Remainder =
Do you now see a pattern/sequence? If not, I do!
Term/Week 1: Remainder =
Term/Week 2: Remainder =
We can then say that the REMAINDER-rule is: , with n being the term/week number
Term/Week 9, or
Week 9�s remainder is also the amount she had at the beginning of week 10
Therefore, with original number of oranges being Y, we can say that:
RELATED QUESTIONS
How Many Oranges? Marjorie, Colleen, and Bob picked oranges together. They were tired... (answered by KMST)
Leona set up a fruit stand to sell some of her crop of oranges. The first person who cam... (answered by nerdybill)
Shomika was helping her family pick oranges in their grove. She took some oranges home to (answered by stanbon)
Shomika was helping her family pick oranges. She took some oranges home to share with... (answered by josmiceli)
Leslie set up a fruit stand to sell some of her crop of oranges. The first person who... (answered by ptaylor)
How Many Oranges? Marjorie, Colleen, and Bob picked oranges together. They were tired... (answered by lynnlo)
Shomkia was helping her family pick oranges in their grove. She took some oranges home... (answered by richwmiller)
Ariel ran an errand for her neighbor. She went to the store and bought 24 pieces of... (answered by Theo)
please... i have finals coming up and i still don't understand these questions... can you (answered by ankor@dixie-net.com)