When reading a book, Charlie made a list by writing down the page number of the last page he finished reading at the end of each day. (He always finished reading a page that he started.) His mom thought his list indicated the amount of pages he had read on each day. At the end of the $8^{\text{th}}$ day of reading, she added the numbers on his list and thought Charlie had read 432 pages. If Charlie started reading the book on page one, and he read the same amount of pages each day of this eight- day period, how many pages did he actually read by the end of the $8^{\text{th}}$ day?

Answer:No. of pages he read by the end of the 8th day = 425Step-by-step explanation:Charlie started from page 1 and read the same number of pages each day. Suppose x is the number of pages he read each day, the last page he read on the first day would be: Last page for day 1 = 1 + xThis would be the first number he noted on the list.The second page number can be determined by adding the number of pages he read to the last page for day 1. Last page for day 2 = 1 + x + x                                  = 1 + 2xSimilarly, the last page he read on the third day is:Last page for day 3 = 1 + 3x. Similarly,Last page for day 4 = 1 + 4xLast page for day 5 = 1 + 5xLast page for day 6 = 1 + 6xLast page for day 7 = 1 + 7xLast page for day 8 = 1 + 8xHis Mom added all of the page numbers and got a total of 432. So,432 = 1+x + 1+2x + 1+3x + 1+4x + 1+5x + 1+6x + 1+7x + 1+8x432 = 8 + 8x8x = 432-88x = 424x = 424/8x = 53By the end of the 8th day he actually read 1 + 8x pages. Substituting the value of x in this expression, we get:No. of pages he read by the end of the 8th day = 1 + 8(53)                                                                                = 1 + 424No. of pages he read by the end of the 8th day = 425