WHAT?! You still haven’t changed to new currency notes yet?! Then where am I going to find the money for your cousin/niece/nephew/babies’ ang paos???!!!
And so by the wrath of her Almighty Dowager Mom, Miss Loi rushed to the banks at her Town Centre to exchange new notes.
But today being the last Friday of the week before Chinese New Year, most banks had already run out of new notes by the time she arrived.
Those with new notes still available were easily distinguished by long snaking queues, along with a security guard who told her, with a pessimistic shake of the head, “There’ll be nothing left to exchange by the time you reach the counter, even if you’re brave enough to join the queue!“.
Thus, like desperate Last-Minute Buddha Foot Huggers looking for tuition centres a week before their exams, Miss Loi joined the ranks of desperate uncles and aunties now roaming aimlessly from bank to bank like a flock of lost sheep.
Just when all hope seemed lost, a grating sound of opening gates was heard from the direction of one of the banks, followed by a shriek from one of the aunties.
In that heart stopping moment, a cat stopped its rummaging activity around a dustbin, and together with Miss Loi and the rest of the uncles and aunties, slowly turned their heads in unison towards the source of the sound …
… just in time to see a bank employee complete the pasting of a notice which basically said
The near-stampede that followed produced some of the most troubling scenes the Town Centre had ever witnessed, as everyone raced like a brigade of troopers towards the bank entrance, charging forward like no tomorrow in the name of duty, honour, and their babies’ 2011 Chinese New Year ang paos.
Just when the tussling horde was within touching distance of the entrance, a bank employee stepped out from behind those glass doors and shouted
Calm down everyone! We only have limited amounts of currency notes, but our bank’s resident Maths Guru have worked out a strategy that will serve as many of you as possible!
Each of you will be given a queue number, and you shall only enter when your number is called!
Please be patient! Your time will come!
From a board that was subsequently put up, the bank had a total of 198 × new $2 notes, 330 × new $10 notes and 132 × new $50 notes available.
To serve as many people and to be as fair as possible, it was decided that the new notes will be distributed in such a way that everyone can only exchange the same number of $2 notes, the same number of $10 notes, and the same number of $50 notes (while stocks last).
- Miss Loi was allocated Queue Number 67. If the queue numbers were called out in an ascending numerical order, should she stick around?
- Find the total value of the notes each person was able to exchange.
Patience my friends! Your time will come! Your time will come!
But will there be anything left for her when her ‘time’ eventually comes?
2 Comments
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HCF of 198, 330 and 132 is 66.
198 = 66 x 3
330 = 66 x 5
132 = 66 x 2
So 66 people can each get 3 $2 notes, 5 $10 notes and 2 $50 notes.
Each person can get 3x$2 + 5x$10 + 2x$50 = $156.
And Miss Loi should stick around in case one of those people whose number lies between 1 and 66 decided that he should go elsewhere to try his luck. 🙂
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@mathslover: "Grandma don't go anywhere! Your time will come! This is a HCF problem!"
Miss Loi turned to find a young boy talking to his granny standing beside her.
"You see, my teacher is currently teaching us the Factors & Multiples topic in class, and I learnt that solving HCF/LCM problems are very straightforward, PROVIDED you know that is a HCF/LCM problem in the first place."
"So the crucial first step is to IDENTIFY whether the chunk of story is a HCF/LCM problem and then DETERMINE whether to use HCF or LCM to solve the problem."
The young boy continued ...
"In this case, we are looking to distribute the $2/$10/$50 notes equally to as many people as we can - this means we are looking for the greatest common number that we can divide the numbers 198, 330 and 132 by."
"And by this definition we're looking at the HCF of 198, 330 and 132! We shouldn't use LCM here since we are trying to divide the three numbers (instead of multiplying)!
Remember:
(in situations when the numbers are to be divided)
(in situations when the numbers are to be multiplied - often used to find instances when two or more events occur at the same time etc.)
"
The boy cleared his throat briefly ...
"You can now find the HCF via straightforward prime factorisation (as mathslover had done):
198 = 2 × 32 × 11
330 = 2 × 3 × 5 × 11
132 = 22 × 3 × 11
⇒ HCF = 2 × 3 × 11 = 66
or via the 'table' method:
⇒ HCF = 2 × 3 × 11 = 66
So the greatest number that we can divide 198, 132 and 330 by is 66
⇒ the bank can distribute the notes equally to a maximum of 66 persons
⇒ each person will get 3 × $2 (198/66) + 5 × $10 (330/66) + 2 × $50 (132/66) = $156 new notes!"
He look at the piece of paper in his granny's hand.
"And so Grandma, with your Queue Number of 66 you'll be the last person who will be served by the bank! See I'm so smart! You better tell Mommy & Daddy to reward me with an iPhone for helping you!"
Just as Miss Loi was about to leave in disappointment, the boy's granny suddenly exclaimed,
"ALAMAK! I forgot to bring my money out! Sigh ... I'm really getting old. Guess we won't be changing any notes today."