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Solving tricky 2009 Maths question
Maths can be a tricky subject to tackle, but it is also an essential part of any student's journey.
In 2009, the PSLE exam had some tough questions that tested students' problem-solving abilities. In this article, we'll tackle one of the most challenging questions.
The 2009 chocolate and sweets question
Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim’s sweets to chocolates became 1:7. The ratio of Ken’s sweets to chocolates became 1:4. How many sweets did Ken buy?
Solution:
Let's suppose Jim purchased X chocolates and Ken purchased Y sweets.
Now, we know that Jim received half of the sweets from Ken and then he ate 12 sweets.
We also know that the ratio of his sweets to chocolate became 1:7.
So, we can say that Jim has \( {Y\over2}-12\) sweets.
Since Jim gave Ken half his chocolates, we know Jim now has \(X-2\) chocolates.
We have been told that after eating 12 chocolates, Jim's sweets to chocolate rato is 1:7.
We can write this algebraically as:
\({{Y\over2}-12\over{X-2}}={1\over7}\)
\({(Y-24)\over X}={1\over 7}\)
\(7(Y-24)=X\)
This is our equation 1.
Now, let's solve for Ken.
Ken bought some sweets and gave half of them to Jim.
So, the number of sweets that Ken has is \(Y\over 2\).
Ken received half the chocolates from Jim, and he ate 18 of them.
So, now Ken has \({x \over 2} - 18\) chocolates.
We also know that after eating the chocolates, Ken's has sweets to chocolates in 1:4 ratio.
So,
\({{Y\over 2}\over {x \over 2} - 18}={1\over 4}\)
\({{Y}\over {x} - 36}={1\over 4}\)
\(4Y = X - 36\)
This is our second equation.
Now, let's put equation 1 (\(7(Y-24)=X\)) and equation 2 (\(4Y = X - 36\)) together.
\(4Y = (7(Y-24) - 36\)
\(4Y = 7Y-168 - 36\)
\(4Y = 7Y-204\)
\(4Y-7Y = -204\)
\(-3Y = -204\)
\(3y = 204\)
\(Y = {204\over 3}\)
\(Y = 68\)
so, Ken bought 68 sweets.
We have provided simple solutions to challenging PSLE Math questions from these years:
