There were some dragonfruits at a mart. In the morning, ¹₆ of dragonfruits were sold. In the afternoon, another 26 dragonfruits were sold. The total number of dragonfruits left was 6 less than ⁵₁₂ of the number of dragonfruits the mart had at first.

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

	Comparison 1	Comparison 2
Before	6x2 =  12 u	12x1 =  12 u
Change 1	- 1x2 = - 2 u
After 1	5x2 =  10 u
Change 2	- 26
After 2	10 u - 26	5x1 - 6 = 5 u - 6

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

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

10 u - 26 = 5 u - 6
10 u - 5 u = 26 - 6
5 u = 20

1 u = 20 ÷ 5 = 4

Number of dragonfruits at first
= 12 u
= 12 x 4
= 48

(b)
Number of dragonfruits that remained unsold
= 10 u - 26
= 10 x 4 - 26
= 40 - 26
= 14

Fraction of dragonfruits that remained unsold
= ¹⁴₄₈
= ⁷₂₄

Answer(s): (a) 48; (b) ⁷₂₄