## Wednesday, December 23, 2015

### [Pri_20151223WNSV] Unravelling Four Whole Numbers

Problem

 If  A,  B,  C  and  D  are whole numbers such that  A × B = 8,  B × C = 28, C × D = 63,  B × D = 36,  find the values of    A,  B,  C  and  D.

Introduction
This question seems to be taken from a secondary school textbook from a chapter on linear equations.  However, I think a good  primary school pupil could attempt this.

Strategy
The key to solving the above problem is to make observations.  When you multiply up the first two equations, you get an  A,  a  C  and two  Bs  in the product.  Hmmm ... This doesn’t look promising ...  Ah!  But when you multiply the second and the third equations together, you get an  B,  a  D  and two  Cs  in the product.  This can cancel (via division) with the fourth equation which has one B  and one  D  in the product.

Solution

Remark
Always cancel as much as possible, to avoid large numbers and reduce chances of making careless mistakes.
By the way, a whole number is a non-negative (zero or positive) integer that does not contain any fractional part.   As such, the set of whole numbers is {0, 1, 2, 3, 4, ...}.  Thus we do not need to consider the negative square roots.

H04. Look for pattern(s)
H05. Work backwards
H10. Simplify the problem

Suitable Levels
Primary School Mathematics (Challenge)
Lower Secondary School Mathematics (Challenge)
* other syllabuses that involve whole numbers
* anyone game for a challenge