Part I first before doing this.)
(Note: You should doAfter Sylvia moves 40% of her saving to Sylvatra's bank account, Sylvia and Sylvanna make a competition for 2 years. Sylvia saves $42 every 3 months, while Sylvanna saves $49 every 4 months. In the end of the first year, the one who have more saving should give 7 1 of her saving into the other's account. In the end of the second year, the one who have more saving will win. Who will win the competition and how much money will she have?
Details and Assumptions: In the end of the first and second year, they count their saving after they save the money.
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After Sylvia moves 4 0 % of her saving, Sylvia will have $ 2 1 0 and Sylvanna will have $ 2 1 0 .
In the end of the first year, Sylvia will save
$ 4 2 × 3 1 2 = $ 1 6 8
while Sylvanna will save
$ 4 9 × 4 1 2 = $ 1 4 7
So, Sylvia must give Sylvanna
7 1 × ( $ 2 1 0 + $ 1 6 8 ) = 7 1 × ( $ 3 7 8 ) = $ 5 4
Then, Sylvia will have $ 3 2 4 and Sylvanna will have $ 4 1 1 .
In the end of the second year, Sylvia will save $ 1 6 8 while Sylvanna will save $ 1 4 7 . So, Sylvia will have $ 4 9 2 and Sylvanna will have $ 5 5 8 . Therefore, Sylvanna will win.
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At the start of the contest they both have 210.
Sylvia saves 42 every 3 months. 42*4=$168
Sylvanna saves 49 every 4 months. 49*3=$147
After 1 year, Sylvia has $378 and Sylvanna has $357
Since Sylvia saved more, Sylvia gives 1/7 of her savings that is $54
so, Sylvia now has $324 and Sylvanna has $411
On the 2nd year, they earn the same
324+168=$492
411+147=$558
So Sylvanna wins with $558.