Rollie borrowed some money from his sister. Their brother wanted to know how much Rollie borrowed, but Rollie wouldn’t tell him. Instead, Rollie gave his brother a riddle.

“Each month, I paid our sister one-third of the amount I still owed her plus an additional $3. At the end of 3 months, I still owed her $3.”

Solve the riddle to find out how much money Rollie borrowed from his sister.
Explain how you arrived at your solution.

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facundo3141592 facundo3141592 · Answer 1 · 2022-04-25T12:45:19+02:00

By working with fractions, we will see that the amount that Rollie borrowed from his sister is $31.50.

Let's say that Rollie borrowed a quantity x.

The first month, Rollie returns one third of x + $3, so now he owes:

x - x/3 - 3 = (2/3)*x - 3

the second month returns another third of what he owes plus $3, so now he returns:

(1/3)*((2/3)*x - 3) + 3 = (2/9)*x + 2

So no he owes:

(2/3)*x - 3 - (2/9)*x - 2 = (4/9)*x - 5

Finally, on the third month he returns:

(1/3)*((4/9)*x - 5) + 3 = (4/27)*x - 5/3 + 3 = (4/27)*x + 4/3

Now he owes:

(4/9)*x - 5 - (4/27)*x - 4/3 = (8/27)*x - 19/3

And that is equal to $3, what he owes at the end of the third month, so we need to solve:

(8/27)*x - 19/3 = 3

(8/27)*x = 3 + 19/3 = 28/3

Solving for x, we get:

x = (27/8)*(28/3) = 31.5

So Rollie borrowed $31.5 from his sister.

If you want to learn more about fractions, you can read:

https://brainly.com/question/11562149