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
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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. ☺☺☺☺
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:
