There were some dragonfruits at a supermarket. In the morning, ¹₆ of dragonfruits were sold. In the afternoon, another 40 dragonfruits were sold. The total number of dragonfruits sold was 9 less than ³₄ of the number of dragonfruits the supermarket had at first.

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

	Comparison 1	Comparison 2
Before	6x2 =  12 u	4x3 =  12 u
Change 1	- 1x2 = - 2 u
After 1	5x2 =  10 u
Change 2	- 40
After 2	10 u - 40	3x3 - 9 = 9 u - 9

(a)
The number of dragonfruits at first is repeated in both comparisons. Make the number of dragonfruits at first.  LCM of 6 and 4 is 12.

The number of dragonfruits in the end is the same in both comparisons.

10 u - 40 = 9 u - 9
10 u - 9 u = 40 - 9
7 u = 49

1 u = 49 ÷ 7 = 7

Number of dragonfruits at first
= 12 u
= 12 x 7
= 84

(b)
Number of dragonfruits that remained unsold
= 3 u + 9
= 3 x 7 + 9
= 30

Fraction of dragonfruits that remained unsold
= ³⁰₈₄
= ⁵₁₄

Answer(s): (a) 84; (b) ⁵₁₄