Eliminate Possibilities Assignment

Question

Sue counted the lines of a page in her book. Counting by threes gave a remainder of 2. Counting by fives also gave a remainder of 2. Counting by sevens gave a remainder of 5. How many lines were on the page? (Here, your answer should be practical – a typical page has fewer than 100 lines.)

Okay, the last type of sample question, there are 5 such on the exam! Thank you for your help. I haven't done these in years! Having some to compare help! 

 

Answer 1

Number of lines, n=(3×5)x+2 for divisibility by 5 and 3 with remainder 2.

15x+2=7y+5, 15x-7y=3, (15x-3)/7=y, 3(5x-1)/7=y

So 5x-1 must be divisible by 7. When x=3, 10, 17, etc., y=6, 21, 36, etc. So n=47, 152.

Since n<100, n must be 47.

 

Answer 2

Thank You very much, Four hor exam today! Phew, I was WAYY off on this one, well I was at least on the right track! Thank you!