The prices of two fruits sold at a supermarket is shown.
| Fruit |
Price |
| Dragonfruits |
6 kg for $8 |
| Lemons |
8 kg for $7 |
- Pierre bought an equal mass of dragonfruits and lemons and spent $77 more on dragonfruits than on lemons. What was the total mass of fruits that Pierre bought?
- Kathy spent an equal amount of money on dragonfruits and lemons. In terms of their masses, what was the ratio of dragonfruits to the ratio of lemons Kathy bought?
(a)
LCM of 6 and 8 = 24
One set = 24 kg of dragonfruits and 24 kg of lemons
Number of sets of 6 kg of dragonfruits
= 24 ÷ 6
= 4
Number of sets of 8 kg of lemons
= 24 ÷ 8
= 3
Difference in price of dragonfruits and lemons in one set
= 4 x 8 - 3 x 7
= 32 - 21
= $11
Number of sets
= 77 ÷ 11
= 7
Mass of dragonfruits and lemons in one set
= 24 + 24
= 48 kg
Total mass of fruits bought
= 7 x 48
= 336 kg
(b)
LCM of 8 and 7 = 56
Number of sets of 6 kg of dragonfruits to be bought with $56
= 56 ÷ 8
= 7
Mass of 7 sets of 6 kg of dragonfruits
= 7 x 6
= 42 kg
Number of sets of 8 kg of dragonfruits to be bought with $56
= 56 ÷ 7
= 8
Mass of 8 sets of 8 kg of lemons
= 8 x 8
= 64 kg
Mass of dragonfruits : Mass of lemons
42 : 64
(÷2) 21 : 32
Answer(s): (a) 336 kg; (b) 21 : 32
