So for the first one, you'll need to write out all the factors of both 30 and 16. (30--1, 2, 3, 5, 6, 10, 15, 30) (16--1, 2, 4, 8, 16) The biggest number that goes into both 30 and 16 is 2.
For the second kne, its the same thing. (48--1, 2, 3, 4, 6, 8, 12, 16, 24, 48) (18--1, 2, 3, 6, 9, 18) The biggest number that can go into both 48 and 18 is 6.
Let the number of chemistry books be x and the number of calculus books be y total number of books in each case is: x+y=24 x=24-y.....i
Weight of each case: 2707.2/20 =135.36 thus 4.2x+6.0y=135.36..ii substituting i in ii 4.2(24-y)+6y=135.36 100.8-4.2y+6y=135.36 hence 1.8y=34.56 y=19.2 hence x=24-19.2 x=4.8 thus the number of chemistry books was 4.8*20=96 number of calculus was 19.2*20 =384 books
