Use the information below to answer the questions
(a) Jane bought 6 books from Bishan Book Shop and paid $90.75. What is the total mass of 6 books that she bought ?
(b) If Jane paid with a $100 note, how much change did she get back after paying the 6 books ?
Solution:
(a) It is a guess-and-check question.
The idea before starting guessing (in general) is to calculate one set of books. Gradually check if one or more sets are still applicable (within the limit of money paid by Jane).
1 set = 1 encyclopedia + 1 dictionary + 1 diary = 3 books
Price of 1 set = $22.75 + $17.50 + $9.25 = $49.50
Money left = $90.75 - $49.50 = $41.25
Jane cannot buy the second set because the money left is less than price of one set of books.
Now we can start guessing for remaining 3 books.
(Guess 1) Let say she bought another encyclopedia (second encyclopedia)
- remainder $41.25 - $22.75 = $18.50
- the money is not enough for third encyclopedia, but enough for second dictionary
- remainder $18.50 - $17.50 = $1
- However, $1 cannot buy another book.
- So this guess is not right !
(Guess 2) Let say after she bought another encyclopedia, she bought one or more diaries
- remainder $18.50 - $9.25 = $9.25
- the money is enough for third diary
- remainder $9.25 - $9.25 = 0
- So exactly total six books bought and no money left !
- Total = 2 encyclopedias + 1 dictionary + 3 diaries
- Total weight = (2*1.02) + 2.07 + (3*0.9) = 6.81 kg
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