**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*B*s 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*C*s 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)

*****

* other syllabuses that involve whole
numbers

* anyone game for a challenge

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