Wednesday, December 23, 2015

[S1_20151221ABEX] The Table as the Years go by ...

Problem

Simon is  15q  years old.  He is now  5  times as old as his son.  How old will he be when his son is  28  years old?

Introduction
     This is an introductory algebra problem, good for getting used to the language of algebra.  As we have seen in this previous article, tabulation is a good way to help organise our information.  Although no one will penalise you for not using tables, once you start using tables, you wonder how you could ever survive without them.
     I present two approaches.  One way is to consider the number of years passed by.  A second way is to observe that the age difference always remains the same as time goes by.

Solution 1


Now
future
Simon
15q
?
Son
3q
28

The number of years passed is  28 – 3q.
Simon’s future age = 15q + (28 – 3q) = 12q + 28

Ans: When the son is  28  years old, Simon will be  (12q + 28)  years old.


Solution 2     (Refer to table as above)

Note that the age gap always remains the same.
Age difference = 15q  – 3q = 12q.
Simon’s future age = 28 + 12q.

Ans: When the son is  28  years old, Simon will be  (12q + 28)  years old.

Remark
     The answer required is an algebraic expression, in terms of  q.  Since we do not know the value of  q,  do not try to evaluate the expression, but just leave it as it is.  When learning algebra, one needs to get comfortable working with unknowns.
     Also remember to be mentally flexible.  There may be more than one way to “skin the cat”.


H02. Use a diagram / model  [tabulation]
H04. Look for pattern(s)
H05. Work backwards
H06. Use before-after concept
H11. Solve part of the problem

Suitable Levels
Lower Secondary Mathematics (Secondary 1)
GCE ‘O’ Level “Elementary” Mathematics (revision)
* other syllabuses that involve ratios and algebra


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