Sarin and his coin bank part 47 (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 Fraction, Percentage, 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.

Read also the posting on Sarin learns the concept of Fraction (mathematics concept) to understand Fraction.

Read the posting on Sarin learns Average Number, Percentage and and Charting in school (Math Concept) to understand the concept of Percentage.

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

Upper primary school mathematics question UPQ484

At first, 25% of Sarin’s money in his coin bank was the same as 1/3 of Hairu’s money in his coin bank. Father gave Hairu another $80 while Sarin spent $150 on some books. In the end, Hairu had 2 ½ times as much money in his coin bank as Sarin had in his coin bank.

(a)        How much money did Sarin have in his coin bank at first?

(b)        How much money did Hairu have in his coin bank in the end?

Solution:

                        25% of Sarin’s money was same as 1/3 of Hairu’s money

                        25% ==> ¼ of a whole

                        The initial model

UPQ484-1

                        Hairu had 2 ½ times more than Sarin, after Hairu received $80 from father and Sarin spent $150

                        The math model for in the end,

UPQ484-2

                        From the model,

                        2 units = 4U – 150 ==> 10 units = 20U – 750

                        5 units = 3U + 80 ==> 10 units = 6U + 160

                        20U – 750 = 6U + 160

                        14U = 910

                        1U = 65

                        The amount of money in Sarin’s coin bank at first = 4 × 65 = $260

                        The amount of money in Hairu’s coin bank in the end = 3 × 65 + 80 = $275

Alternative solution:

                        25% of Sarin’s money was same as 1/3 of Hairu’s money

                        25% ==> ¼ of a whole

                        The ratio at first,

                        Sarin’s money : Hairu’s money = 4 : 3

                        Sarin spent $150 on books and Hairu got $80 from father

                        Sarin’s money : Hairu’s money = (4U – 150) : (3U + 80)

                        Hairu’s money was 2 ½ times of Sarin’s money in the end

                        The final ratio,

                        Sarin’s money : Hairu’s money = 1 : 2.5 = 10 : 25 = 2 : 5

                        1 unit ==> (4U – 150)/2 = 2U – 75

                        1 unit ==> (3U + 80)/5

                        2U – 75 = (3U + 80)/5

                        5 × (2U – 75) = 3U + 80

                        10U – 375 = 3U + 80

                        7U = 375 + 80 = 455

                        1U = 65

                        The amount of money in Sarin’s coin bank at first = 4 × 65 = $260

                        The amount of money in Hairu’s coin bank in the end = 3 × 65 + 80 = $275

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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