Question 4 - Figure it out - Page 93, 94, 95 - Chapter 4 Class 7 - Another Peek beyond the Point (Ganita Prakash II)

Transcript

Question 4 A teacher placed textbooks that are 2.5 cm thick on a bookshelf. The teacher wanted to place 80 textbooks on the shelf. The bookshelf is 160 cm long. How many books could be placed on the shelf? Was there any space left? If yes, how much?First, let us find how much space 80 textbooks take Space 80 textbooks take Since each book is 2.5 cm Space taken by 80 textbooks = Number of textbooks × Thickness of each book = 80 × 2.5 = 80 × 25/10 = 8 × 25 = 200 cm Given bookshelf is 160 cm long Since 200 cm > 160 cm, thus 80 books will not fit in the shelf Let’s now find how many books can fit in the bookshelf Number of books that can fit in the bookshelf Since each book is 2.5 cm, and bookshelf is 160 cm long Number of books in bookshelf = (𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝐵𝑜𝑜𝑘𝑠ℎ𝑒𝑙𝑓)/(𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝐸𝑎𝑐ℎ 𝑏𝑜𝑜𝑘) = 𝟏𝟔𝟎/(𝟐.𝟓) Converting into fractions = 160 × 1/2.5 = 160 × 1/(25/10) = 160 × 10/25 = 160 × 2/5 = 32 × 2 = 64 Thus, 64 books can fit in the bookshelf Now, we need to answer Was there any space left? If yes, how much? Space left If she only puts the 64 books that fit, there is 0 cm left (it's a perfect fit for 64). However, if she tries to put 80, she is short by 16 books × 2.5 cm = 40 cm of shelf space.