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

Fruit	Price
Grapefruits	4 kg for $14
Starfruits	6 kg for $8

1. Mark bought an equal mass of grapefruits and starfruits and spent $78 more on grapefruits than on starfruits. What was the total mass of fruits that Mark bought?
2. Tiffany spent an equal amount of money on grapefruits and starfruits. In terms of their masses, what was the ratio of grapefruits to the ratio of starfruits Tiffany bought?

(a)
LCM of 4 and 6 = 12

One set = 12 kg of grapefruits and 12 kg of starfruits

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

Number of sets of 6 kg of starfruits
= 12 ÷ 6
= 2

Difference in price of grapefruits and starfruits in one set
= 3 x 14 - 2 x 8
= 42 - 16
= $26

Number of sets
= 78 ÷ 26
= 3

Mass of grapefruits and starfruits in one set
= 12 + 12
= 24 kg

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

(b)
LCM of 14 and 8 = 56

Number of sets of 4 kg of grapefruits to be bought with $56
= 56 ÷ 14
= 4

Mass of 4 sets of 4 kg of grapefruits
= 4 x 4
= 16 kg

Number of sets of 6 kg of grapefruits to be bought with $56
= 56 ÷ 8
= 7

Mass of 7 sets of 6 kg of starfruits
= 7 x 6
= 42 kg

Mass of grapefruits : Mass of starfruits 
16 : 42 _(÷2)
8 : 21

Answer(s): (a) 72 kg; (b) 8 : 21