A student decides to save money every week according to the following plan: she saves Rs. 50 in the first week and increases her saving by a fixed amount Rs. d each subsequent week. After some weeks, she has saved a total of Rs. 4550, and her saving in the last of those weeks was Rs. 300.
(i) Form an equation in d and the number of weeks k using the information about the last week’s saving.
(ii) Using the total amount saved, write a second equation in k and solve the two equations simultaneously to find d and k.
(iii) If she continues the same pattern, determine the total amount she will have saved at the end of 2k weeks.