The prices of two fruits sold at a supermarket is shown.
| Fruit |
Price |
| Dragonfruits |
6 kg for $10 |
| Grapefruits |
4 kg for $4 |
- Henry bought an equal mass of dragonfruits and grapefruits and spent $40 more on dragonfruits than on grapefruits. What was the total mass of fruits that Henry bought?
- Kylie spent an equal amount of money on dragonfruits and grapefruits. In terms of their masses, what was the ratio of dragonfruits to the ratio of grapefruits Kylie bought?
(a)
LCM of 6 and 4 = 12
One set = 12 kg of dragonfruits and 12 kg of grapefruits
Number of sets of 6 kg of dragonfruits
= 12 ÷ 6
= 2
Number of sets of 4 kg of grapefruits
= 12 ÷ 4
= 3
Difference in price of dragonfruits and grapefruits in one set
= 2 x 10 - 3 x 4
= 20 - 12
= $8
Number of sets
= 40 ÷ 8
= 5
Mass of dragonfruits and grapefruits in one set
= 12 + 12
= 24 kg
Total mass of fruits bought
= 5 x 24
= 120 kg
(b)
LCM of 10 and 4 = 20
Number of sets of 6 kg of dragonfruits to be bought with $20
= 20 ÷ 10
= 2
Mass of 2 sets of 6 kg of dragonfruits
= 2 x 6
= 12 kg
Number of sets of 4 kg of dragonfruits to be bought with $20
= 20 ÷ 4
= 5
Mass of 5 sets of 4 kg of grapefruits
= 5 x 4
= 20 kg
Mass of dragonfruits : Mass of grapefruits
12 : 20
(÷4) 3 : 5
Answer(s): (a) 120 kg; (b) 3 : 5
