Wednesday, March 9, 2011

Chapter 4: Algebra Puzzle

Attempt the Algebra Puzzle at: http://www.mathplayground.com/algebra_puzzle.html

  • There are 2 levels.
  • Attempt the 3x3 grid until you are able to find the solution of the puzzle.
  • Present your solution (together with the screen capture that shows the answers are correct) in your personal blog.
  • Label the Blog post as "Chapter 4: Algebra Puzzle"
  • Post the permlink of your post to comments in this post.
  • The 3x4 grid is a bonus level... It is not compulsory, do challenge yourself to see if you could solve it using algebra (see example below)
The objective of the puzzle is to...
  • Find the value of each of the three objects presented in the puzzle.
  • The numbers given represent the sum of the objects in each row or column.
  • Sometimes, only one object will appear in a row or column.
  • That makes the puzzle easier to solve. Other times, you will have to look for relationships among the objects.

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Here is an example of how you should articulate your solutions in your personal blog
The 3 x 3 Grid puzzle

My solution (Method 1, which most of you would use this method to reason out/deduce your answer):
  • 3 Apples = 6
  • Therefore, 1 Apple represents 2
  • 1 Apple + 2 Cars = 4
  • Since 1 Apple represents 2,
  • 2 + 2 Cars = 4
  • 2 Cars represent 2
  • Therefore, 1 Car represents 1
  • 2 Apples + 1 Pen = 20
  • Since 1 Apple represents 2, 2 Apples = 4
  • 4 + 1 pen = 20
  • Therefore, 1 Pen represents 16
My solution (Method 2, using the algebraic method which you will learn in Chapter 6, in Term 2):
  • Let a represents apple
  • Let c represents car
  • Let p represents pen
  • 3a = 6
  • a = 6/3
  • Therefore, a = 2
  • Since 2a + p = 20
  • 2(2) + p = 20
  • 4 + p = 20
  • p = 20 - 4
  • Therefore, p = 16
  • Since c + 2a = 5
  • c + 2(2) = 5
  • c + 4 = 5
  • c = 5 - 4
  • Therefore, c = 1
In conclusion, each apple represents 2, each pear represents 16and each car represents 1.

Bonus Level (We will only cover this method in next year):

  • Let m represents ice-cream
  • Let p represents pear
  • Let f represents flower
  • 2m + p = 24 {equation #1}
  • m + 2p = 45 {equation #2}
  • From equation #2, we can say m = 45 - 2p
  • Substitute it into equation 1, we get 2(45 - 2p) + p = 24
  • We get 90 - 4p+ p = 24
  • 90 - 3p = 24
  • - 3p = 24 - 90
  • - 3p = - 66
  • Therefore, p = 22
  • m = 45 - 2(22)
  • Therefore, m = 1
  • 2m + f = 26
  • 2(1) + f = 26
  • 2 + f = 26
  • f = 26 - 2
  • Therefore, f = 24
In conclusion, each ice cream represents 1, each pear represents 22 and each flower represents 24.

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