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

Fruit	Price
Passion Fruits	3 kg for $10
Persimmons	6 kg for $4

1. Asher bought an equal mass of passion fruits and persimmons and spent $32 more on passion fruits than on persimmons. What was the total mass of fruits that Asher bought?
2. Kathy 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 Kathy bought?

(a)
LCM of 3 and 6 = 6

One set = 6 kg of passion fruits and 6 kg of persimmons

Number of sets of 3 kg of passion fruits
= 6 ÷ 3
= 2

Number of sets of 6 kg of persimmons
= 6 ÷ 6
= 1

Difference in price of passion fruits and persimmons in one set
= 2 x 10 - 1 x 4
= 20 - 4
= $16

Number of sets
= 32 ÷ 16
= 2

Mass of passion fruits and persimmons in one set
= 6 + 6
= 12 kg

Total mass of fruits bought
= 2 x 12
= 24 kg

(b)
LCM of 10 and 4 = 20

Number of sets of 3 kg of passion fruits to be bought with $20
= 20 ÷ 10
= 2

Mass of 2 sets of 3 kg of passion fruits
= 2 x 3
= 6 kg

Number of sets of 6 kg of passion fruits to be bought with $20
= 20 ÷ 4
= 5

Mass of 5 sets of 6 kg of persimmons
= 5 x 6
= 30 kg

Mass of passion fruits : Mass of persimmons 
6 : 30 _(÷6)
1 : 5

Answer(s): (a) 24 kg; (b) 1 : 5