Hairu shares his stickers part 35 (Math Question)

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The blog postings are about the Singapore Math. The readers can learn from the postings on Solving Singapore Primary School Mathematics. The blog presenting the Math Concept, Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids will learn the skills of dealing with Math Question Solving, Math Modeling and Problem Sums 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, Fraction, Percentage and Problem Sum.

You can read the postings on Sarin learns concept of ratio in school and Sarin learns the concept of Fraction (mathematics concept) to understand the concept of Ratio and Fraction or Portion.

You should read the posting on Sarin learns Average Number, Percentage and Charting in school (Math Concept) to understand about Average Number.

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

Upper primary school mathematics question UPQ313

Hairu had 80 more stickers than Sarin. Hairu gave 25% of his stickers to Sarin. Sarin in return gave 60% of his stickers to Hairu. In the end, Hairu had 100 stickers more than Sarin. How many stickers did Hairu have at first?

 Solution:

             Start the model base on Hairu had 80 more than Sarin 

 

            25% of hairu’s stickers is ¼ fraction of his stickers and we can subdivide the above block by 4

            Redraw the model with Sarin received ¼ fraction of Hairu stickers

 

 

            Sarin gave back 60% of his stickers to Hairu that is given 3/5 fraction of Sarin’s stickers

            Hairu finally had 100 stickers more than Sarin

            The final model

 

 

            From the final model

                        4 units = 100 + 8 – 72 = 36

                        1 unit = 9

                        The number of stickers that Hairu had at first = 4 × 9 + 80 = 116

            Check:

                        Sarin had at first = 4 × 9 = 36

                        25% of Hairu = 116 × 0.25 = 29

                        Give to Sarin, Sarin had = 36 + 29 = 65

                        60% of Sarin had = 65 × 0.6 = 39

                        Hairu finally had = 39 + 116 – 29 = 126

                        Sarin finally had = 65 – 39 = 26

                        Hairu had 126 – 26 = 100 more stickers than Sarin finally

Alternative solution(1):

            By ratio method

            Initial ratio, Hairu had 80 more stickers than Sarin

                        Hairu : Sarin = (4U + 80) : 4U

            Hairu shifted 25% or ¼ fraction of stickers to Sarin

                        Hairu : Sarin = (3U + 60) : (4U + 1U + 20) = (3U + 60) : (5U + 20)

            Sarin gave back 60% or 3/5 fraction of stickers to Hairu

            Final ratio

                        Hairu : Sarin = (3U + 60 + 3U + 12) : (2U + 8) = (6U + 72) : (2U + 8)

            The different in stickers finally is 100

                        6U + 72 – 2U – 8 = 100

                        4U = 36

                        1U = 9

                        The number of stickers Hairu had at first = 4 × 9 + 80 = 116

Alternative solution(2):

            By equations,

            Set: The number of sticker Hairu had at first = D

                   The number of stickers Sarin had at first = J

            Initially,

            D = J + 80

            Finally,

            75%D + 60% (J + 25%D) = 40% (J + 25%D) + 100

            0.75D + 0.2J + 0.05D = 100

            8D + 2J = 1000

            Solve the equations,

            8J + 640 + 2J = 1000

            10J = 360

            J = 36

            The number of stickers Hairu had at first = D = J + 80 = 36 + 80 = 116  

More Questions on Problem Sum. Click here….

More Questions on Fraction and Ratio. Click here….

More Questions on Percentage. Click here….

 

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