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

Fruit	Price
Grapefruits	3 kg for $15
Peaches	4 kg for $7

1. David bought an equal mass of grapefruits and peaches and spent $117 more on grapefruits than on peaches. What was the total mass of fruits that David bought?
2. Nicole spent an equal amount of money on grapefruits and peaches. In terms of their masses, what was the ratio of grapefruits to the ratio of peaches Nicole bought?

(a)
LCM of 3 and 4 = 12

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

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

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

Difference in price of grapefruits and peaches in one set
= 4 x 15 - 3 x 7
= 60 - 21
= $39

Number of sets
= 117 ÷ 39
= 3

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

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

(b)
LCM of 15 and 7 = 105

Number of sets of 3 kg of grapefruits to be bought with $105
= 105 ÷ 15
= 7

Mass of 7 sets of 3 kg of grapefruits
= 7 x 3
= 21 kg

Number of sets of 4 kg of grapefruits to be bought with $105
= 105 ÷ 7
= 15

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

Mass of grapefruits : Mass of peaches 
21 : 60 _(÷3)
7 : 20

Answer(s): (a) 72 kg; (b) 7 : 20