Question

Anna and Hannah have \$80$80dollar sign, 80 each. Their friend offered to invest their money, promising to return a sum rrr times as great as what they invested. Anna was suspicious, so she invested \$20$20dollar sign, 20 only, but Hannah invested her entire \$80$80dollar sign, 80. Fortunately, the friend did indeed return a sum rrr times as great to each.

They decided to make another investment. This time, Hannah invested all of the money returned to her, and Anna invested the money returned to her and the remaining \$60$60dollar sign, 60. Again, they got a sum rrr times as great as what they invested. In the end, Hannah had twice the amount Anna had.
Write an equation in terms of rrr that models the situation.

Answer 1

9514 1404 393

Answer:

2r(20r +60) = 80r^2

Explanation:

Anna's first investment:

20

Anna's first return:

20r

Anna's second investment:

20r +60

Anna's second return:

r(20r +60)

__

Hannah's first investment:

80

Hannah's first return, and her second investment:

80r

Hannah's second return:

80r^2

__

Twice Anna's return was equal to Hannah's return:

2r(20r +60) = 80r^2