The blog postings are about the Singapore Math. The readers can learn from the postings about Solving Singapore Primary School Mathematics. The blog presents the Math Concept, the Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids can aquire the skills of dealing with the Math Modeling, the Math Problem Solving and the Problem Sum from Lower Primary School to Upper Primary School level after reading the blog postings. This posting is an upper primary school math question on Ratio and Problem Sum.

Read the posting on **Fatimah and Hairu play Congkak** to know about Congkak game.

Read the posting on **Sarin learns the concept of Ratio (mathematics concept)** to understand Ratio.

*Challenge yourself with the question before look for the given solution‼!*

**Upper primary school mathematics question UPQ468**

After a few rounds of Congkak game, both Fatimah and Hairu have some marbles in their boxes. The ratio of the number of red marbles to the number of blue marbles in Fatimah’s box is 3 : 1. The ratio of the number of red marbles to the number of blue marbles in Hairu’s box is 2 : 3. There are twice as many marbles that in Fatimah’s box than Hairu’s box.

(a) What is the ratio of the number of red marbles in Fatimah’s box to the number of red marbles in Hairu’a box?

(b) 60 red marbles are added into Hairu’s box after another round of Congkak game and the ratio of the number of red marbles to the number of blue marbles in Hairu’s box becomes 4 : 1. How many blue marbles are there in Hairu’s box?

* *Solution:

There are twice as many marbles in Fatimah’s box than Hairu’s box

Based on the ratio of Red marbles and blue marbles in their boxes

Draw the model

From the model

The ratio of number of red marbles in Fatimah’s box to the number of red marbles in Hairu’s box = 15 : 4

Added 60 red marbles into Hairu’s box, and the ratio of red marbles to blue marbles in Hairu’s box = 4 : 1

Draw the model

In Hairu’s box

From the model

10 units = 60

1 unit = 6

The number of blue marble in Hairu’s box = 3 × 6 = 18

Alternative Solution:

The ratio,

In Fatimah’s box, Redf : Bluef : Boxf = 3 : 1 : 4 = 15 : 5 : 20

In Hairu’s box, Redh : Blueh : Boxh = 2 : 3 : 5 = 8 : 12 : 20

Since the marbles in Fatimah’s is twice as much as Hairu’s box

The ratio, Boxf : Boxh = 2 : 1 = 40 : 20

Redf : Bluef : Redh : Blueh = 2 × 15 : 2 × 5 : 8 : 12 = 30 : 10 : 8 : 12

The ratio of number of red marbles in Fatimah’s box to the number of red marbles in Hairu’s box = 30 : 8 = 15 : 4

In Hairu’s box,

The initial ratio, Redh : Blueh = 2 : 3

The final ratio after added 60 red marbles, Redh : Blueh = 4 : 1 = 12 : 3

Since no change in blue marbles,

The different in Red marble interm of units = 12 – 2 = 10 units

10 units = 60

1 unit = 6

The number of blue marbles in Hairu’s box = 3 × 6 = 18