# A family in Singapore part 60 (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, the Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids will able to acquire knowledge 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 and  Problem solving.

Read also the posting on Sarin learns the concept of Ratio in School (mathematics concept) to understand the concept of Ratio.

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

Upper primary school mathematics question UPQ563

Sarin, Hairu and Fatimah took their parents out for a dinner. If Sarin paid for the dinner, the amount of money that Sarin, Hairu and Fatimah left will be in the ratio 3 : 8 : 9 respectively. If Fatimah paid for the dinner, the amount of money Sarin, Hairu and Fatimah left would be in the ratio 5 : 4 : 1 respectively. If Hairu paid for the dinner, the amount of money Sarin, Hairu and Fatimah left would be in the ratio 10 : 1 : 9 respectively. Sarin had \$40 more than Hairu. How much did the dinner cost?

Solution:

Disregarding of who paid for the dinner, the left over amount is the same.

If Sarin Paid,

Sarin : Hairu : Fatimah : Total = 3 : 8 : 9 : 20

If Fatimah Paid,

Sarin : Hairu : Fatimah : Total = 5 : 4 : 1 : 10 = 10 : 8 : 2 : 20

If Hairu Paid,

Sarin : Hairu : Fatimah : Total = 10 : 1 : 9 : 20

When Fatimah paid, Sarin and Hairu need not to pay for the dinner,

The ratio of their money is the original amount

Sarin has \$40 more than Hairu

The difference = \$40 = 2 units

1 units = \$20

When Sarin paid,

The amount he paid in units = 10 – 3 = 7 units

The dinner cost = 7 × 20 = \$140