Sarin and his coin bank part 39 (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, 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.

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

Upper primary school mathematics question UPQ401

Hairu had 5/7 as much money in his coin bank as compare to Sarin’s money in his coin bank. After each of them deposited \$154 into their bank accounts, Hairu had 7/12 as much money in his coin bank as compare to Sarin’s money in the coin banks. How much did Sarin have at first in his coin bank?

Solution:

Hairu had 7/12 as much money as Sarin after each of them deposited \$154 into their bank accounts

If we added back the \$154 to each of them, Hairu were had 5/7 as much money as Sarin

Draw the model

Per the model

11units = 154

1 unit = 14

The amount of money Sarin had at first = 14 × 35 = \$490

Alternative Solution(1):

The model

Based on the model

(7H + 154)/5 = (12H + 154)/7

7×(7H + 154) = 5×(12H + 154)

49H + 7 × 154 = 60H + 5 × 154

11H = 2 × 154 = 308

1H = 28

The amount of money Sarin had at first = 12 × 28 + 154 = \$490

Alternative Solution(2):

Express using Ratio

Original ratio

Hairu : Sarin = 5 : 7

Deduct \$154 from each of them to get Final ratio

Final ratio

Hairu : Sarin = 7 : 12 = (5U – 154) : (7U – 154)

(5U – 154)/(7U – 154) = 7/12

12(5U – 154) = 7(7U – 154)

60U – 12 × 154 = 49U – 7 × 154

11U = 5 × 154

1U = 70

The amount of money Sarin had at first = 7 × 70 = \$490