A family in Singapore part 33 (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 will able to acquire knowledge of dealing 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 Fraction and Problem Sum.

You can click here and read the posting on A family in Singapore about Sarin’s family.

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

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

Upper primary school mathematics question UPQ321

Sarin and Hairu had some money. Sarin’s money was $80 more than Hairu. After Sarin spent 1/4 of his money and Hairu spent 1/3 of his money, Sarin still had $83 more than Hairu. How much money did Hairu have at first?

 Solution:

            Sarin had $80 more than Hairu at first

            The initial Math Model

 

 

            Saroin spent 1/4 of his money and Hairu spent 1/3 of his money

            Redraw the model by portion Sarin’s money to 4 equal portions and Hairu’s money to 3 equal portions

 

 

            Subdivide the blue unit blocks to 4 × 3 = 12 equal units

 

 

            After both of them spend the amount, Sarin still has $83 more than Hairu

            The model can be rearrange with the amount spent included as shown

 

 

            Per the model

            1 unit + 60 = 83

            1 unit = 83 – 60 = $23

            The amount of money Hairu had at first = 12 × 23 = $276

Alternative Solution(1):

By equations,

            Set S as money that Sarin had at first

            Set H as money that Hairu had at first

            Sarin had $80 more than Hairu at first

            S = H + 80

            After Spending, Sarin more than Hairu by $83

            Sarin spent 1/4 fraction of his money and left with 3/4 fraction of money

            Hairu spent 1/3 fraction of his money and left with 2/3 fraction of money

            3/4 S = 2/3 H + 83

            S = 8/9 H + 83 × 4/3

            H + 80 = 8/9 H + 83 × 4/3

            1/9 H = 83 × 4/3 – 80

            H = 9 × 83 × 4/3 – 9 × 80 = $276

            The amount of money Hairu had at first was $276

Alternative Solution(2):

            Set H as Hairu’s money at first

            Sarin’s money = H + 80

            Sarin spent 1/4 fraction of his money

            Sarin left = 3/4 fraction of his money = 3/4 × (H + 80)

            Hairu spent 1/3 fraction of his money

            Hairu left = 2/3 × H

            After spending, Sarin had $83 more than Hairu

            3/4 × (H + 80) – 2/3 × H = 83

            3/4 H – 2/3 H = 83 – 3/4 × 80

            1/12 H = 83 – 60 = 23

            H = 12 × 23 = 276

            The amount of money Hairu had at first = 12 × 23 = $276

More Questions on Fraction & Ratio. Click here….

 More Questions on Problem Sum. Click here…

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