Wednesday, April 26, 2017

[Pri5 20170426FEM] Baking Éclairs and Macaroons

Problem / Question
This problem for primary 5 from one of my acquaintances on Facebook, considered to be of intermediate level difficulty (in Singapore).  But it looks rather challenging to draw all those bar diagrams, doesn’t it?
Here is my quickie solution without explicit algebra and without bar diagrams.

Solution
For convenience, we use 6 circle units for Eclairs and 6 square units for Macaroons.
Suppose there were half as many Eclairs and Macaroons, then there would be 15 more Eclairs.  So 3 square units add 15 can be changed to 3 circle units.
Add 15 to the 17 and change 3 square units to 2 circle units.  We deduce that 5 circle units is the same as 85.  From here we can easily figure out the rest.

Ans: 102 éclairs.

Comment
The problem can be solved by bar diagrams.  However, there are many ways to skin the cat.  For more good stuff, please join my Facebook group “Effective and Elegant Mathematics”.

H02. Use a diagram / model
H05. Work backwards
H06. Use before-after concept
H08. Make suppositions
H09. Restate the problem in another way
H11. Solve part of the problem

Suitable Levels
Primary School / Elementary School Mathematics
* any precocious or independent learner who is interested