7 Lana and Betty managed to save $160 each. Their friend offered to invest their money, promising to return a sum k times as large as what they invested. Lana
was suspicious, so she invested $40 only, but Betty invested her entire $160. Fortunately, their friend did indeed return a sum k times as large to each.
They decided to make another investment. Betty invested her entire savings plus earning, and Lana invested her initial investment plus earnings and the
remaining $120. Again, they got a sum ke times as large as what they invested. In the end, Betty had twice the amount Lana had.
Write an equation to find the value of k.
What is the value of k?