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
No comments:
Post a Comment
Note: Only a member of this blog may post a comment.