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

Fruit	Price
Starfruits	2 kg for $15
Passion Fruits	4 kg for $4

1. Sean bought an equal mass of starfruits and passion fruits and spent $104 more on starfruits than on passion fruits. What was the total mass of fruits that Sean bought?
2. Xandra spent an equal amount of money on starfruits and passion fruits. In terms of their masses, what was the ratio of starfruits to the ratio of passion fruits Xandra bought?

(a)
LCM of 2 and 4 = 4

One set = 4 kg of starfruits and 4 kg of passion fruits

Number of sets of 2 kg of starfruits
= 4 ÷ 2
= 2

Number of sets of 4 kg of passion fruits
= 4 ÷ 4
= 1

Difference in price of starfruits and passion fruits in one set
= 2 x 15 - 1 x 4
= 30 - 4
= $26

Number of sets
= 104 ÷ 26
= 4

Mass of starfruits and passion fruits in one set
= 4 + 4
= 8 kg

Total mass of fruits bought
= 4 x 8
= 32 kg

(b)
LCM of 15 and 4 = 60

Number of sets of 2 kg of starfruits to be bought with $60
= 60 ÷ 15
= 4

Mass of 4 sets of 2 kg of starfruits
= 4 x 2
= 8 kg

Number of sets of 4 kg of starfruits to be bought with $60
= 60 ÷ 4
= 15

Mass of 15 sets of 4 kg of passion fruits
= 15 x 4
= 60 kg

Mass of starfruits : Mass of passion fruits 
8 : 60 _(÷4)
2 : 15

Answer(s): (a) 32 kg; (b) 2 : 15