Question

Anna and Hannah have $80 each. Their friend offered to invest their money, promising to return a sum r times as great as what they invested. Anna was suspicious, so she invested $20 only, but Hannah invested her entire $80. Fortunately, the friend did indeed return a sum r 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. Again, they got a sum r times as great as what they invested. In the end, Hannah had twice the amount Anna had.

Write an equation in terms of r that models the situation.

Answer 1

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