Question

When starting a new unit, a teacher announces that each day after the first, the class must do twice the total number of problems that had been assigned on all previous days. The class works for 6 days and on the 7th day she says that this is our last day of the unit. On that last day, what fraction of the problems do they still have to complete?

Answer 1

We have that

x-------------- number of problems that had been assigned the first day

problems to complete

day total

1 ------------------x---------------------------------------------------x

2------------------(x)*2----------------------------------------------2x

3------------------(x+2x)*2-----------------------------------------6x

4------------------(x+2x+6x)*2-----------------------------------18x

5------------------(x+2x+6x+18x)*2-----------------------------54x

6 -----------------(x+2x+6x+18x+54x)*2-----------------------162x

7 -----------------( x+2x+6x+18x+54x+162x)*2--------------486x

486x-162x=324x problems to resolve last day

324/486=2/3

The fraction of the problems do they still have to complete on that last day is 2/3