Given that there are 2849 more English books than Chinese books i.e. difference between English and Chinese books is 2849

Transcription

1 Problem 1: 3/4 of the books in the library are English books and the rest are Chinese books. There are 2849 more English books than Chinese books. What is the total number of books in the library? Let X be the total number of books in the library Given that ¾ of the books are English books # of English books = ¾ X Given that rest of the books are Chinese books # Chinese books = Total books - # of English books # of Chinese books = X - ¾ X = ¼ X Given that there are 2849 more English books than Chinese books i.e. difference between English and Chinese books is 2849 Difference between English and Chinese books = # of English Books - # of Chinese Books 2849 = ¾ X ¼ X or 2849 = ½ X X = 2 (2849) = 5698 Total books in the library = 5698 books

2 Problem 2: A full tin of paint just by itself has a mass of 27 kg. When the same tin is 2/5 filled with paint, it has a mass of 12 kg. What is the mass of the empty tin? Given that mass of a full tin of paint by itself (i.e. without the tin) is 27 kg Mass of 2/5 tin of paint by itself = (27) = = 10.8 Kg It is given that mass of a tin filled 2/5 with paint = 12 kg. This includes the mass of tin + mass of paint. 12 = Mass of empty tin + Mass of paint 12 = Mass of empty tin Mass of empty tin = 1.2 Kg

3 Problem 3: Rani read 52 pages of a book on Monday. On Tuesday, she read 1/6 of the remaining pages. If she still had half of the book left to be read, how many pages were there in the book? Let X be the total number of pages in the book # of pages read on Monday = 52 pages # of remaining pages = X-52 Given that Rani reads 1/6 of the remaining pages on Tuesday # of pages read on Tuesday = (Remaining Pages) = (X-52) At the end of Tuesday she has half the books still remaining = Total number of pages remaining at end of Tuesday = Total pages pages read on Monday pages read on Tuesday So we can write = X 52 - (X-52). Solving for X with this equation = or 3X = 5X-260 or 2X = 260 or X = 130 So the total number of pages in the book = 130

4 Problem 4: Raja sold 1/4 of his eggs on Saturday and 1/6 of the remainder on Sunday. If he had 140 eggs left, how many eggs did he have at first? Let X be the number of eggs that Raja has Given that Raja sold ¼ of his eggs on Saturday Number of Eggs sold on Saturday = # of Eggs Remaining = Total - # sold on Saturday = X - = Given that Raja Sells 1/6 of the remaining eggs on Sunday # of Eggs sold on Sunday = (Remaining eggs) = ( = Given that he has 140 eggs left after Sunday # of Eggs left after Sunday = Total Eggs Eggs sold on Saturday Eggs sold on Sunday Substituting number of eggs sold on Saturday and Sunday from equation 1 and 2 in the above equation 140 = X - - LCM is 8 for the right side of the equation. 140 = or 1120 = 5X or X = 224 So Raja had 224 eggs to begin with

5 Problem 5: In a country, 7/10 of the people are Chinese. 2/3 of the remainder are Malay and the rest are Indians. If there are 60,000 Indians, how many Chinese are there? Let X be the number of people in the Country Given that 7/10 of the people are Chinese # of people who are Chinese = # of Remaining people (includes Malaya and Indians) = Total - # of people who are Chinese = X - = Given that 2/3 rd of the remaining people are Malaya # of people who are Malaya = (# of Remaining People) = ( = Given that rest of the people are Indians and there are 60,000 Indians. # of Indians = Total - # of people who are Chinese - # of people who are Malaya Substituting the # of Chinese and Malays from 1 and 2 in the above equation we get 60,000 = X - - LCM for the above equation is 10. We can write 60,000 = or 600,000 = 10X-9X or X = 600,000 So the total population is 600,000 From equation 1, # of Chinese = Substituting X = 600,000 in the above equation we get # of Chinese = 420,000

6 Additional Problems: There are some pens in a box. 1/3 of them are black, 1/2 of them are red and the rest are green. If there are 35 green pens, how many pens are there altogether? 2/5 of Raja's money can buy 40 books. How many books can he buy with 3/4 of his money Rani has 372 beads. 1/6 are blue and the rest are red. How many more red beads are there than blue beads?