Chap 6: Algebra Puzzle - Solving Equations (Preview)

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.
• 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.