Sarin and his coin bank part 41 (Math Question)

Standard

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, Algebra 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 Sarin learns Symbol, Algebra and Equation in school (Math Concept) to understand the concept of Algebra.

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

Upper primary school mathematics question UPQ412

Sarin and Hairu have some money in their coin banks. If Sarin gives $20 to Hairu, he will have thrice as much money as Hairu. If Hairu gives $16 to Sarin, he will have 1/9 of what Sarin has. How much money does Sarin have at first?

Solution:

            Two conditions given and based on the conditions to put up the model

            Start with Sarin’s money is 3 times Hairu’s money after he gives $20 to Hairu

            Determine the amount they have at first

            Add the inform of Sarin’s money is 9 times Hairu’s money after he receives $16 from Hairu

            Determine the relationship of the two conditions in the model

UPQ412-1

            From the model

                        9U = 3 × (1U + 20 + 16) + 20 + 16

                        9U = 3U + 144

                        6U = 144

                        1U = 24

            The amount of money Sarin has at first = 9 × 24 – 16 = $200

            The amount of money Hairu has at first = 24 + 16 = $40

            To check:

                        Sarin gives Hairu $20

                        Sarin’s money = 200 – 20 = $180

                        Hairu’s money = 40 + 20 = $60

                        180 ÷ 60 = 3

                        Sarin’s money is 3 times of Hairu’s money

                        Hairu gives Sarin $16

                        Sarin’s money = 200 + 16 = $216

                        Hairu’s money = 40 – 16 = $24

                        216 ÷ 24 = 9

                        Sarin’s money is 9 times of Hairu’s money

Alternative Solution(1):

            By using algebra and equations

            Set S as the amount of money Sarin has at first

            Set H as the amount of money Hairu has at first

            Base on condition 1

                        Sarin gives $20 to Hairu

                        Sarin’s money = (S – 20)

                        Hairu’s money = (H + 20)

                        Given that Sarin’s money is thrice of Hairu’s money

UPQ412-2

                        S – 20 = 3 × (H + 20) = 3H + 60

                        S = 3H + 80

            Based on condition 2

                        Hairu gives $16 to Sarin

                        Sarin’s money = (S + 16)

                        Hairu’s money = (H – 16)

                        Given that Hairu’s money is 1/9 fraction of Sarin’s money

UPQ412-3

                        S + 16 = 9 × (H – 16) = 9H – 144

                        S = 9H – 160

                        Solve the two equations

                        S = 3H + 80

                        S = 9H – 160

                        3H + 80 = 9H – 160

                        6H = 240

                        H = 40

                        S = 3 × 40 + 80 = $200

                        The amount of money sarin has at first = $200

Alternative Solution(2):

            Using Ratio method

            The final ratio  after Sarin gives $20 to Hairu, Sarin’s is thrice as many as Hairu’s money

            Sarin’s money : Hairu’s money  = S : H = 3 : 1

            To tack back the $20 to get the original ratio

                        S : H = (3U + 20) : (1U – 20)

            If Hairu gives $16 to Sarin,

                        S : H = (3U + 20 + 16) : (1U – 20 – 16) = (3U + 36) : (1U – 36)

            Based on the raito of Sarin’s money to Hairu’s money is 9 : 1

                        3U + 36 = 9 × (1U – 36)

                        3U + 36 = 9U – 324

                        6U = 360

                        1U = 60

            The amount of money Sarin has at first = 3 × 60 + 20 = $200

More Questions on Problem Sum. Click here….

More Questions on Ratio. Click here….

More Questions on Algebra and Equations. Click here…..

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s