**Question**

This problem can be solved with Primary
School knowledge using ratios. The
famous Singapore

*bar diagramming method*can be used to model the situation, but I prefer my own**. The former method is good for visualisation for beginners, while the latter is faster if you want to solve it quickly without fussing around drawing the perfect diagram. My DRU method is also visual in another way, and it works with big numbers as well as small numbers. Alternatively, this can be solved using***Distinguished Ratio Units***via simultaneous equations.***algebra***Solution 1**(Using my Distinguished Ratio Units method) [H02]

**Explanation:**Since the number of white balls is a multiple of 3, I let “triangle” 3 represent the number of white balls. I let “heart” 1 represent the number of red balls. There are 50 more white balls than red balls. [H04] When the white balls are removed three at a time, the number of groups of three would be one-third of the number of white balls, i.e. 1 triangle unit. [H04] This number is less than the number of red balls (1 heart unit) by 50. So 1 triangle unit plus 50 gives 1 heart unit. [H04] Following on from the heart to the “triangle” 3, one realises that 2 “triangle” units is the same as 100. [H05] So one triangle unit is 50. [H11] From here we can solve the rest of the problem.

**Solution 2**(using Algebra) [H13, H05]

*w*=

*k*+ 50 = 3

*h*–––––––––– [1]

*r*=

*k*=

*h*+ 50 –––––––––– [2]

for some
unknown

*k*and*h*. And then [1] – [2] gives [H10]*w*–

*r*= 50 = 2

*h*– 50

so 2

*h*= 50 + 50*h*= 50

This
quickly leads to

*w*= 150

and

*r*= 100.
H02. Use a
diagram / model

H04. Look for
pattern(s)

H05. Work
backwards

H09. Restate
the problem in another way

H10. Simplify
the problem

H11. Solve part
of the problem

H13* Use
Equation / write a Mathematical Sentence

**Suitable Levels**

*****Primary School Mathematics (“Ratio”)

*****

* other syllabuses that involve ratio or algebra

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