There were some passion fruits at a supermarket. In the morning, ¹₄ of passion fruits were sold. In the afternoon, another 30 passion fruits were sold. The total number of passion fruits sold was 9 less than ⁵₇ of the number of passion fruits the supermarket had at first.

1. How many passion fruits were there at first?
2. What fraction of the passion fruits in the supermarket remained unsold in the afternoon?

	Comparison 1	Comparison 2
Before	4x7 =  28 u	7x4 =  28 u
Change 1	- 1x7 = - 7 u
After 1	3x7 =  21 u
Change 2	- 30
After 2	21 u - 30	5x4 - 9 = 20 u - 9

(a)
The number of passion fruits at first is repeated in both comparisons. Make the number of passion fruits at first.  LCM of 4 and 7 is 28.

The number of passion fruits in the end is the same in both comparisons.

21 u - 30 = 20 u - 9
21 u - 20 u = 30 - 9
13 u = 39

1 u = 39 ÷ 13 = 3

Number of passion fruits at first
= 28 u
= 28 x 3
= 84

(b)
Number of passion fruits that remained unsold
= 8 u + 9
= 8 x 3 + 9
= 33

Fraction of passion fruits that remained unsold
= ³³₈₄
= ¹¹₂₈

Answer(s): (a) 84; (b) ¹¹₂₈