Every algebra teacher is bombarded with the same question every year, “What will I ever use this algebra stuff for?”
Well here is a sample algebra problem that you can use to respond to these insidious questions, along with proving to your students that there is no magic or mystery when algebra is used.
Algebra Problem
Step 1 - Write down the year you were born. [P}
Step 2 - Write down a year when a memorable event took place in your life. [Q]
Step 3 - Write down your age as the last day of this year. [Y-P]
Step 4 - Write down the number of years since the memorable event (Step 2) took place. [Y-Q]
Step 5 - Add the 4 numbers obtained in Steps 1 through 4. [P + Q + (Y - P) + (Y - Q) = 2Y]
Every student will have the answer 2Y = 4018 or Y = 2009 (or what ever the current year is when calculating)
How does this work?
P +Q + (Y - P) + ( Y - Q) = P + Q + Y - P + Y - Q (parentheses removed)
= P- P + Q - Q + Y + Y (rearranging the terms)
= 2Y ( P’s and Q’s cancel each other out)
= 4018 (when Y = 2009)
In other words, the number in Step 1 combined with that in Step 3, deleted the number in Step 1, giving the current year, 2009; similarly, the number in Step 2 combined with that in Step 4, deleted the number in Step 2, giving, once again, the current year, 2009. Hence, adding all the 4 numbers from Step 1 through Step 4 effectively deleted every number other than twice the current year, 2009, giving the result of 2 x 2009 = 4018! (Note that most number puzzles undo what has been done, so as to “force” a certain result, as can be easily proved by using deductive logic or by using algebra.)
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Tags: algebra challenges, algebra problem solving, solving math problems
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