Sarin and his coin bank part 43 (Math Question)

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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 learn 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 Solving.

You can read the posting on Sarin and his coin bank for the story of coin bank.

Read the posting on Sarin learns concept of ratio in school to understand Ratio.

Challenge yourself with the Question before look out for the given solution‼!

Upper primary school mathematics question UPQ428

The ratio of Hairu’s money to Sarin’s money in their coin banks was 3 : 4 at first. After Hairu gave Sarin $24, the ratio of Hairu’s money to Sarin’s money became 1 : 2. What was the total amount of money they had altogether?

Solution:

            The initial ratio of their money

            Hairu : Sarin = 3 : 4 and After Hairu gave Sarin $24, the ratio = 1 : 2

UPQ428-1

            From the ratio model

                        1 unit = 24 + 12 = $36

                        Total = 7 × 36 = $252

Alternative Solution(1):

            By using ratio

            The total amount no change

            Initial ratio,

                        Hairu : Sarin : Total = 3 : 4 : 7 = 9 : 12 : 21

            The final ratio,

                        Hairu : Sarin : Total = 1 : 2 : 3 = 7 : 14 : 21

            The amount given by Hairu to Sarin in term of units = 9 – 7 = 2

                        2 units = 24

                        1 unit = 12

            The total of money they have in their coin banks = 21 × 12 = $252

Alternative Solution(2):

            The final ratio,

                        Hairu : Sarin = 1 : 2

            Add back $24 to Hairu and deduct $24 from Sarin to get to initial ratio

            The initial ratio,

                        Hairu : Sarin = (1U + 24) : (2U – 24) = 3 : 4

            Therefore,

                        4 × (1U + 24) = 3 × (2U – 24)

                        4U + 96 = 6U – 72

                        2U = 168

                        1U = 84

            The total amount no change and in term of units = 1U + 2U = 3U

            The total amount of their money in their coin banks = 3 × 84 = $252

More Questions on Problem Sum. Click here….

More Questions on Ratio. Click here….

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