Challenging P6 Ratio Question Solved Fast: Total Did Not Change Explained

Looking for help with a challenging ratio word problem from Singapore Math? This Primary Mathematics question has puzzled many students, especially when it comes to applying the “total did not change” concept. Below is a real question that one of our students posted using the on-demand homework help feature.

Question:
Darren, Muthu and Hafiz shared the cost of a gift equally using their savings. Darren saved $36 more than Muthu. If Darren paid for the gift first, the ratio of Darren’s remaining savings to Muthu’s savings to Hafiz’s savings would be 4 : 9 : 11. If Muthu paid for the gift first, the ratio of Darren’s savings to Muthu’s remaining savings to Hafiz’s savings would be 12 : 1 : 11. If Hafiz paid for the gift first, the ratio of Darren’s savings to Muthu’s savings to Hafiz’s remaining savings would be 4 : 3 : 1. How much did the gift cost?

This question shows how complex ratio problems can be simplified by breaking them into clear scenarios and applying the “total did not change” concept. With the right approach, even a challenging question like this becomes manageable. Keep reading to see how a student solved it step by step with a mentor through instant homework help.

Real mentors, Real-time answers

Zand Toh

P6 Mathematics
hello!
May I help u with your question
hi can you help me with this?
okk so firstly this qn have 3 scenarios
darren pay first, muthu pay first and hafiz pay first
so in each scenario after each of them pay, the money left will still be the same
so all the ratios should have the same unit
Is it all must be 12 units?
all must be 24 units
4:9:11 adds up to 24 unit
ok noted
so if u write out all the ratios
u will find out that the gift is 8 units
can you show me the working?
and 3 units = 36 because darren has 36 more than muthu
can u see the 3rd scenario where hafiz pay
darren has 12 units and muthu has 9 units of savings, so 36 = 3 units
any qn to clarify
ok thank you for the detailed explanation :)
ok no worries! Will end the sess now without any qn
yes thank you

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