Sarin and his coin bank part 40 (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 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.

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

Upper primary school mathematics question UPQ411

In Sarin’s coin bank, there are some 20₵ and 50₵ coins. The ratio of the number of 20₵ coins to the number of 50₵ coins is 5 : 6. After 80 of 20₵ coins are removed and 15 of 50₵ coins are added, the ratio becomes 2 : 3. Find the sum of money in the coin bank at first.

Solution:

At first the ratio of the number of 20₵ to 50₵ is 5 : 6

When removed 80 of 20₵ coins and added 15 of 50₵ coins, the ratio = 2 : 3

Rearange the 50₵ block and determine the equalivalent of 2U

Redraw the 20₵ block with 2U information added in

Per the model

1 unit = 5 + 5 + 80 = 90 coins

Number of 20₵ coins at first = 5 × 90 = 450

Number of 50₵ coins at first = 6 × 90 = 540

Total value in the coin bank at first = 450 × 0.2 + 540 × 0.5 = \$360

Alternative Solution(1):

Base on the combine model

Per the above model

5 parts ==> 2U + 80

6 parts ==> 3U – 15

30parts ==> 12U + 480

30parts ==> 15U – 75

12U + 480 ==> 15U – 75

3U ==> 555

1U ==> 185

20₵ at first in the coin bank = 2 × 185 + 80 = 450

Value of 20₵ coins in the coin bank at first = 450 × 0.2 = \$90

50₵ at first in the coin bank = 3 × 185 – 15 = 540

Value of 50₵ coins in the coin bank at first = 540 × 0.5 = \$270

Total value in the coin bank = 270 + 90 = \$360

Alternative Solution(2):

By ratio

The number ratio at first

20₵ : 50₵ = 5 : 6

To remove 80 20₵ and add 15 50₵

20₵ : 50₵ = (5U – 80) : (6U + 15) = 2 : 3

3 × (5U – 80) = 2 × (6U + 15)

15U – 240 = 12U + 30

3U = 270

1U = 90

20₵ at first in the box = 5 × 90 = 450

Value of 20₵ coins in the coin bank at first = 450 × 0.2 = \$90

50₵ at first in the coin bank = 6 × 90 = 540

Value of 50₵ coins in the coin bank at first = 540 × 0.5 = \$270

Total value in the coin bank = 270 + 90 = \$360