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You can read the postings on **Sarin’s family celebrating Hari Raya Puasa** and **Sarin’s family and Ramadan** in Welcome page about story of Sarin’s family during Ramadan and Hari Raya Puasa.

To read also the postings on **Sarin learns the concept of Fraction (mathematics concept)** and **Sarin learns concept of ratio in school** to understand the concept of Fraction and Ratio.

*Challenge yourself with the question before look out for the given solution‼*

**Upper primary school mathematics question UPQ295**

Fatimah prepared a basket of apples for the guests on Hari Raya Puasa. There were 112 fewer red apples than green apples in the basket. 1/4 of the red apples and 3/8 * *of the green apples were consumed by the guests. The number of green apples left was twice as many as the number of red apples left. How many apples Fatimah prepared in the basket at first?

Solution:

Start with the final number of green apples was twice the number of red apples, than include the number of green apples and reda apples sold into the model

The math model

From the model

3 × 11U – 5 × 1U = 112

28U = 112

1U = 4

The number of red apples in the basket at first = 4 × 5 × 4 = 80

The number of green apples in the basket at first = 11 × 3 × 4 = 192

The total number of apples that Fatimah prepared at first = 80 + 192 = 272

Alternative Solution(1) :

Start with the condition of Green apples is 112 more than Red apples. Take red apples as 1U to make the ratio

Initial ratio

Green apples : Red apples = (1U + 112) : 1U

After ¼ fraction of red apples and 3/5 of the green apples ate by guests

The final ratio on apples left in the basket is

Green apples : Red apples = 5/8 (1U + 112) : 3/4 × 1U = (5/8 U + 14) = 3/4 U

Given that the final ratio, Green apples : Red apples = 2 : 1

5/8 U + 14 × 5 = 2 × 3/4 U = 3/2 U

3/2 U – 5/8 U = 14 × 5

14/16 U = 14

1U = 16 × 5 = 80

Total number of apples prepared by Fatimah = 2U + 112 = 2 × 80 + 112 = 272

Alternative solution(2):

Start with the final ratio

Green apples : Red apples = 2 : 1

The remaining green apples is 5/8 fraction of original

The remaining red apples is 3/4 fraction of original

The original ratio (at first)

Green apples : Red apples = 2 × 8/5 : 1 × 4/3 = 16/5 : 4/3

Green apples : Red apples = 48/15 : 20/15 = 48 : 20 = 24 : 10

The different = 14 units

14 units = 112

1 unit = 8

The number of apples prepared by Fatimah at first = 8 × 34 = 272