The prices of two fruits sold at a supermarket is shown.
| Fruit |
Price |
| Kiwis |
2 kg for $8 |
| Mangosteens |
3 kg for $7 |
- Riordan bought an equal mass of kiwis and mangosteens and spent $70 more on kiwis than on mangosteens. What was the total mass of fruits that Riordan bought?
- Kimberly spent an equal amount of money on kiwis and mangosteens. In terms of their masses, what was the ratio of kiwis to the ratio of mangosteens Kimberly bought?
(a)
LCM of 2 and 3 = 6
One set = 6 kg of kiwis and 6 kg of mangosteens
Number of sets of 2 kg of kiwis
= 6 ÷ 2
= 3
Number of sets of 3 kg of mangosteens
= 6 ÷ 3
= 2
Difference in price of kiwis and mangosteens in one set
= 3 x 8 - 2 x 7
= 24 - 14
= $10
Number of sets
= 70 ÷ 10
= 7
Mass of kiwis and mangosteens in one set
= 6 + 6
= 12 kg
Total mass of fruits bought
= 7 x 12
= 84 kg
(b)
LCM of 8 and 7 = 56
Number of sets of 2 kg of kiwis to be bought with $56
= 56 ÷ 8
= 7
Mass of 7 sets of 2 kg of kiwis
= 7 x 2
= 14 kg
Number of sets of 3 kg of kiwis to be bought with $56
= 56 ÷ 7
= 8
Mass of 8 sets of 3 kg of mangosteens
= 8 x 3
= 24 kg
Mass of kiwis : Mass of mangosteens
14 : 24
(÷2) 7 : 12
Answer(s): (a) 84 kg; (b) 7 : 12
