The Sister's Saving, Part II

Algebra Level pending

(Note: You should do Part I first before doing this.)

After 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 $\frac {1}{7}$ 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.

Sylvanna, $558.00 Sylvanna, $597.00 Sylvia, $597.00 Sylvia, $558.00

2 solutions

Emmanuel David
Apr 30, 2014

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.

Mu'amar Musa Nurwigantara
Apr 5, 2014

After Sylvia moves $40$ % of her saving, Sylvia will have $\$210$ and Sylvanna will have $\$210$ .

In the end of the first year, Sylvia will save

$\$42 \times \frac {12}{3} = \$168$

while Sylvanna will save

$\$49 \times \frac {12}{4} = \$147$

So, Sylvia must give Sylvanna

$\frac {1}{7} \times (\$210 + \$168) = \frac {1}{7} \times (\$378) = \$54$

Then, Sylvia will have $\$324$ and Sylvanna will have $\$411$ .

In the end of the second year, Sylvia will save $\$168$ while Sylvanna will save $\$147$ . So, Sylvia will have $\$492$ and Sylvanna will have $\$558$ . Therefore, Sylvanna will win.

The Sister's Saving, Part II

2 solutions

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