walking through 3 gates 2 friends have to leave 1/4 of their money at each gate. how much money did they have at the start to have $648 left
A is the starting amount
(3A/4) after the first gate
A(3/4)^2 after the second gate...
so
A(3/4)^3=648
A= 648*4*4*4/27=648*64/27= ...
To determine how much money the two friends had at the start, we need to work backward from the remaining $648.
Let's break down the process step by step:
1. At the third gate, both friends have to leave 1/4 of their money. Since they have $648 remaining, this means they collectively had $648 * 4 = $2592 before reaching the third gate.
2. Before the third gate, they each had $2592 / 2 = $1296.
3. At the second gate, they also have to leave 1/4 of their money. Therefore, prior to reaching the second gate, they collectively had $1296 * 4 = $5184.
4. Before the second gate, they each had $5184 / 2 = $2592.
5. Finally, at the first gate, they once again have to leave 1/4 of their money. So, before reaching the first gate, they collectively had $2592 * 4 = $10368.
6. Before the first gate, they each had $10368 / 2 = $5184.
Therefore, the two friends initially had $5184 each.