Sarin’s family celebrating Hari Raya Puasa part 10 (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 presenting the Math Concept, Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids can acquire the skills to deal with Math Modeling, Math Problem Solving and 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, Fraction and Problem Sum.

You can read the postings on Sarin’s family celebrating Hari Raya Puasa and Sarin’s family and Ramadan in Welcome page about story of Sarin’s family during Ramadan and Hari Raya Puasa.

To read also the postings on Sarin learns the concept of Fraction (mathematics concept) and Sarin learns concept of ratio in school to understand the concept of Fraction and Ratio.

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

Upper primary school mathematics question UPQ295

Fatimah prepared a basket of apples for the guests on Hari Raya Puasa. There were 112 fewer red apples than green apples in the basket.  1/4 of the red apples and 3/8  of the green apples were consumed by the guests. The number of green apples left was twice as many as the number of red apples left. How many apples Fatimah prepared in the basket at first?

Solution:

            Start with the final number of green apples was twice the number of red apples, than include the number of green apples and reda apples sold into the model

            The math model

 

 

 

 

            From the model

                                    3 × 11U – 5 × 1U = 112

                                    28U = 112

                                    1U = 4

                        The number of red apples in the basket at first = 4 × 5 × 4 = 80

                        The number of green apples in the basket at first = 11 × 3 × 4 = 192

                        The total number of apples that Fatimah prepared at first = 80 + 192 = 272

Alternative Solution(1) :

                        Start with the condition of Green apples is 112 more than Red apples. Take red apples as 1U to make the ratio

                        Initial ratio

                        Green apples : Red apples = (1U + 112) : 1U

                        After ¼ fraction of red apples and 3/5 of the green apples ate by guests

                        The final ratio on apples left in the basket is

                        Green apples : Red apples = 5/8 (1U + 112) : 3/4 × 1U = (5/8 U + 14) = 3/4 U

                        Given that the final ratio, Green apples : Red apples = 2 : 1

                        5/8 U + 14 × 5 = 2 × 3/4 U = 3/2 U

                        3/2 U – 5/8 U = 14 × 5

                        14/16 U = 14

                        1U = 16 × 5 = 80

                        Total number of apples prepared by Fatimah = 2U + 112 = 2 × 80 + 112 = 272

Alternative solution(2):

                        Start with the final ratio

                        Green apples : Red apples = 2 : 1

                        The remaining  green apples is 5/8 fraction of original

                        The remaining red apples is 3/4 fraction of original

                        The original ratio (at first)

                        Green apples : Red apples = 2 × 8/5 : 1 × 4/3 = 16/5 : 4/3

                        Green apples : Red apples = 48/15 : 20/15 = 48 : 20 = 24 : 10

                        The different = 14 units

                        14 units = 112

                        1 unit = 8

                        The number of apples prepared by Fatimah at first = 8 × 34 = 272

  More Questions on Problem Sum. Click here….

More Questions on Fraction and Ratio. Click here…

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