Paul had some pomegranates and dragonfruits. The number of pomegranates and dragonfruits left were the same after Paul sold ¹₂ of the pomegranates and ⁴₇ of the dragonfruits. If he had 78 pomegranates at first,

1. How many pomegranates were left?
2. How many dragonfruits did Paul have at first?

	Pomegranates	Dragonfruits
Before	2x3 = 6 u	7 u
Change	- 1x3 = - 3 u	- 4 u
After	1x3 = 3 u	3 u

(a)
Fraction of the pomegranates left
= 1 - ¹₂
= ¹₂

Fraction of the dragonfruits left
= 1 - ⁴₇
= ³₇

The number of pomegranates and dragonfruits left were the same.  Make the number of pomegranates and dragonfruits left the same. LCM of 1 and 3 is 3.

Number of pomegranates at first = 6 u
Number of dragonfruits at first = 7 u

6 u = 78

1 u = 78 ÷ 6 = 13

Number of pomegranates left
= 3 u
= 3 x 13
= 39

(b)
Number of dragonfruits at first
= 7 u
= 7 x 13
= 91

Answer(s): (a) 39; (b) 91