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

Fruit	Price
Mangosteens	5 kg for $9
Grapefruits	4 kg for $6

1. Lee bought an equal mass of mangosteens and grapefruits and spent $24 more on mangosteens than on grapefruits. What was the total mass of fruits that Lee bought?
2. Rachel spent an equal amount of money on mangosteens and grapefruits. In terms of their masses, what was the ratio of mangosteens to the ratio of grapefruits Rachel bought?

(a)
LCM of 5 and 4 = 20

One set = 20 kg of mangosteens and 20 kg of grapefruits

Number of sets of 5 kg of mangosteens
= 20 ÷ 5
= 4

Number of sets of 4 kg of grapefruits
= 20 ÷ 4
= 5

Difference in price of mangosteens and grapefruits in one set
= 4 x 9 - 5 x 6
= 36 - 30
= $6

Number of sets
= 24 ÷ 6
= 4

Mass of mangosteens and grapefruits in one set
= 20 + 20
= 40 kg

Total mass of fruits bought
= 4 x 40
= 160 kg

(b)
LCM of 9 and 6 = 18

Number of sets of 5 kg of mangosteens to be bought with $18
= 18 ÷ 9
= 2

Mass of 2 sets of 5 kg of mangosteens
= 2 x 5
= 10 kg

Number of sets of 4 kg of mangosteens to be bought with $18
= 18 ÷ 6
= 3

Mass of 3 sets of 4 kg of grapefruits
= 3 x 4
= 12 kg

Mass of mangosteens : Mass of grapefruits 
10 : 12 _(÷2)
5 : 6

Answer(s): (a) 160 kg; (b) 5 : 6