[Pri20150503RTB] Specky Men & Women

Question

Introduction

     This looks like a difficult problem because there are different fractions and different numbers.   There seems to be so much information.  How do we deal with that?

Solution

     One good way to organise information is to use a two-way table.  I have a row for the “speckies” (bespectacled people) and a row for the “non-speckies”.  I put one column for the ladies and one column for the men.  Put in column- and row- totals and the grand total.  Instead of spelling out the words, I use icons to represent the different groups.  Who says you cannot be creative in maths?

     I use “circle” units for the women and “square” units for the men.  This is my Distinguished Ratio Units method.  It is easy to work out the total for the speckies.  Just subtract  282  from  456.  After filling up the table, we get a diagram like this:-

Notice the  1  “circle” unit?  It is easy to multiply this by  5  so as to match the  5  “circle” units.  So I multiply everything from the speckies’ row by  5.  I am imagining what would happen if there were five times as many bespectacled men and women.  For then the numbers of bespectacled women would be the same as the number of the clear-sighted women.  The result is shown in green below.

With the “circle” units equalised to  5  units each, we can now compare the  25 “square” units with the  4  “square” units.  The difference of  21 “square” units must be due to the difference between 870 and 282, which is  588.  That allows us to work out the value of  1  “square” unit and then  5  “square” units (representing the number of male speckies).  Knowing two of the numbers in the speckies’ row, we can finally work out the remaining number, which is the number of female speckies.

Ans:   34 women wear spectacles.

Summary

     In this article, I have demonstrated the use of Distinguished Ratio Units and the use of tables for organising information.  I have also demonstrated the technique of equalising one type of units (in this case the “circle” units), so that we can compare the other type of units  (here the “square” units).  I hope you have found this article useful.

Heuristics Used

H02. Use a diagram / model

H04. Look for pattern(s)

H05. Work backwards

H08. Make suppositions

H11. Solve part of the problem

Suitable Levels

* Primary School Mathematics

* other syllabuses that involve whole numbers and ratios