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 beforeafter 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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