The prices of two fruits sold at a supermarket is shown.

Fruit	Price
Passion Fruits	3 kg for $15
Persimmons	4 kg for $8

1. Japheth bought an equal mass of passion fruits and persimmons and spent $108 more on passion fruits than on persimmons. What was the total mass of fruits that Japheth bought?
2. Gwen spent an equal amount of money on passion fruits and persimmons. In terms of their masses, what was the ratio of passion fruits to the ratio of persimmons Gwen bought?

(a)
LCM of 3 and 4 = 12

One set = 12 kg of passion fruits and 12 kg of persimmons

Number of sets of 3 kg of passion fruits
= 12 ÷ 3
= 4

Number of sets of 4 kg of persimmons
= 12 ÷ 4
= 3

Difference in price of passion fruits and persimmons in one set
= 4 x 15 - 3 x 8
= 60 - 24
= $36

Number of sets
= 108 ÷ 36
= 3

Mass of passion fruits and persimmons in one set
= 12 + 12
= 24 kg

Total mass of fruits bought
= 3 x 24
= 72 kg

(b)
LCM of 15 and 8 = 120

Number of sets of 3 kg of passion fruits to be bought with $120
= 120 ÷ 15
= 8

Mass of 8 sets of 3 kg of passion fruits
= 8 x 3
= 24 kg

Number of sets of 4 kg of passion fruits to be bought with $120
= 120 ÷ 8
= 15

Mass of 15 sets of 4 kg of persimmons
= 15 x 4
= 60 kg

Mass of passion fruits : Mass of persimmons 
24 : 60 _(÷12)
2 : 5

Answer(s): (a) 72 kg; (b) 2 : 5