Question
Introduction
This is a
question about percentages, which are really fractions based upon 100 as
denominator. For example, 60%
just means 60/100. It is
possible to solve this using some sort of algebraic
approach based on 100 units for a percentage. However it is more convenient to use fractions
in their lowest terms. I present a
solution based on my Distinguished Units Method, which is a proto-algebraic approach.
Solution
Note
that 60% = 60/100
= 3/5 and 25% = 1/4. The Lowest Common Multiple (LCM) of the
denominators is 20. I use
20 “square” units for the original number of erasers and 20 “circle” units for the original number of pens. This makes the units easy to divide. It does not matter what shape you use to
envelop the different units, as long as different shapes are used for different
types of units.
Ans:
There were 240 pens at first.
Since the question asks for the original number of
pens, it is a good idea to equalise the eraser’s “square” units. Multiplying the first row numbers by 8/20 gives 8
“square” units for the third rows.
This serves as a stepping stone to connect the “circle” units. See the part highlighted in yellow. From
8 “circle” units to 15
“circle” units, the difference is
84. This allows us to deduce the
value of 1 “circle” unit. The original number of pens is represented
by 20
“circle” units corresponds to 240, which is the answer we want.
Final Remarks
It is a
good idea to know the fractions of some of the more common percentages. For example,
25% = 1/4, 50% = 1/2, 75% = 3/4
20% = 1/5, 40% = 2/5, 60% = 3/5 , 80% = 4/5
The usage of
LCM of the denominators is very effective for making calculations easy.
H02. Use a
diagram / model
H04. Look for
pattern(s)
H06. Use
before-after concept
H09. Restate
the problem in another way
H10. Simplify
the problem
H11. Solve part
of the problem
Suitable Levels
* Primary School Mathematics
* other syllabuses that involve whole
numbers and ratios
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