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Jannis and Rohaan from Long Bay Primary School
sent us the following explanation:
1. First we need to make
one change to make the whole problem ridiculously easy.
First we noticed, you have 'double it' and 'halve it' this brings
you back to your original number, but as you have 'add ten' in the
middle of 'double it' and 'halve it' you must add five because 'add
ten' is before 'halve it'.
So now we have:
- Take away you original number
As you can see you are just adding five to your original number
then taking away your original number which is five.
2. First we need to make a
few changes to simplify the whole problem.
'Double the amount' and 'Multiply the result by 1/4 of 20'
effectively is 'multiply by 10'.
But since 'Add the first odd prime number to the new total' is
before 'Multiply the result by 1/4 of 20' you just need to multiply
the first odd prime number by 5 (3 times 5 is 15).
But since you have to subtract 6 (the lowest common multiple of 2
and 3) you may as well add 9 instead of 15 (15 -6 = 9).
So now we have:
So then when you take off the last digit you are effectively
subtracting 9.
What you are left with is 10 times the original number.
3. To explain it, you must
first take off 'Add on today's date' and 'Finally subtract 5 times
today's date'.
This is because after you add on the date you multiply it by 5 and
you then 'subtract 5 times today's date'.
Then you may as well also change 'Multiply it by 1/5 of 100' and
'Multiply by 20% of 25' to 'multiply it by 100' because it is
effectively the same thing as above.
So now you have:
- Now add on your shoe size.
This effectively gives you two places after your age to add on your
shoe size.
Gabriel Tan from Catholic High School used
algebra to explain how these tricks work:
For the first trick:
Let x be the number my friend was thinking of.
1. x .........................Think of a number
2. 2x ........................Double it
3. 2x+10 .................Add 10
4. x+5 ......................Halve it
5. 5 .........................Take away your original number
And there you have it - 5.
For the second trick:
Let x be the amount of money my friend has.
1. x ...............................Double the amount
2. 2x+3 .........................Add the fist odd prime number (3)
to the new total
3. 10x+15 .....................Multiply the result by 1/4 of 20
4. 10x+9 .......................Subtract the lowest common multiple
of 2 and 3
5. 10x ...........................Take off the last digit
And there you have it - the amount x.
For the third trick:
Let x be my friend'??s age, y be today'??s date, and z be the shoe
size.
1. x ..............................Write down your age
2. 20x ..........................Multiply it by 1/5 of 100
(20)
3. 20x+y ......................Add on today's date
4. 100x+5y ..................Multiply by 20% of 25 (5)
5.100x+5y+z ...............Now add on your shoe size
6. 100x+z ....................Finally subtract 5 times today's
date
And there you have it - the amounts x and z.