Help fast Luke and Owen have \$100$100dollar sign, 100 each. Their friend offered to invest their money, promising to return a sum rrr times as great as what they invested. Luke was suspicious, so he invested \$10$10dollar sign, 10 only, but Owen invested his entire \$100$100dollar sign, 100. Fortunately, the friend did indeed return a sum rrr times as great to each.
They decided to make another investment. This time, Owen invested all of the money returned to him, and Luke invested the money returned to him and the remaining \$90$90dollar sign, 90. Again, they got a sum rrr times as great as what they invested. In the end, Owen had \$337.50$337.50dollar sign, 337, point, 50 more than Luke.
Write an equation in terms of rrr that models the situation.