[Pri20150308CSR] Charitable Savings Ratios?

Question

Introduction

     Here is another one of those Singapore Mathematics problems that are two-variable simultaneous equations in disguise.  The key to solving this question quickly is to exploit the fact that the amount of donations are the same in this case.

Solution

     First, read the question and translate the information into a diagram [H02. Use a diagram / model].  I use different shapes (e.g. circle and square) to envelop the different types of units.

     Since we have ‘-80’  for both Sharon and Ryan [H04. Look for pattern(s)], we may deduce that 1 ‘circle’ unit  (5 minus 4 ‘circle’ units) is equal to 3 ‘square’ units (10 minus 7 ‘square’ units).  That means 5 ‘circle’ units is 15 ‘square units’.  [ H10. Simplify the problem]

     By comparison again, we realise that 5 square units is 80 [H05. Work backwards] and hence 15 ‘square’ units is 240.

Ans: Sharon’s savings was $240 at first.

Check

Before    $240   $192      5 : 4

After      $160   $112     10 : 7

Solution makes sense.

Heuristics Used

H02. Use a diagram / model

H04. Look for pattern(s)

H05. Work backwards

H10. Simplify the problem

[Pri20150306APC] Apples-with-Pears Comparison

Question

Introduction

     This question involves money and looks rather challenging, because there are a few unknown quantities.  To solve it, we use the concept of unit costs, so that we can make an “apples-to-apples” ... er ... I mean “pears-to-apples” J comparison of the prices.

Solution

     Since absolute dollar amounts are given, we can quickly solve [H11. Solve part of the problem] for the total costs of pears and apples as follows [H02. Use a diagram / model]:-

     Now we know that the total cost (in dollars) of pears is 45 and for the apples it is 50 (5 more than 45).  Although we do not know the absolute numbers of pears and apples, we know their ratio.  So let us write these down as, say, ‘square’ units. 

     Dividing the total costs by the numbers gives the unit costs, which we know only in ratio terms.  So let us use, say, ‘circle’ units to denote these.  But we know that the unit cost (in $) of an apple is 0.50 less than that of a pear.  And that is equivalent to 5 ‘circle’ units.  From here [H05. Work backwards], we quickly work out the cost of a pear (15 ‘circle’ units) as $1.50.

     Ta da!

Heuristics Used

H02. Use a diagram / model

H05. Work backwards

H11. Solve part of the problem