Challenge+Problem+Rework

I chose to use excel to rework this challenge problem and display each step of the problem with a visual diagram.

Problem: When I received my paycheck, I immediately put 1/3 of it in my savings account. I spent 2/3 of the remaining money on a book I'd been waiting to read. Then, I spent 1/4 of the rest on chocolate. In the end, I had $4.50 left. How big was my paycheck? Explain how you know.

First, I created a representation of the paycheck by filling in 27 squares in excel. I then took 1/3 of that rectangle, representing the portion that went into savings. I then filled in a rectangle to represent the remaining money left from the paycheck.



Then, I repeated the process with the portion taken from the paycheck for the book. The remainder from the last step was carried into this step and 2/3 of it was taken to use toward the book. After subtracting the amount for the book there is a new remainder of the paycheck left over.



Then, 1/4 of the previous remainder was spent on chocolate, which is portrayed below.



The problem states that $4.50 is remaining at the end. So this last remainder is equal to $4.50.



Since there are 4.5 boxes filled and they represent $4.50. This means that each box is equal to a dollar. This tells us that the amount of the original paycheck is equal to the original number of boxes, which was 27, so the answer is $27. The original paycheck was $27.