The prices of two fruits sold at a supermarket is shown.
| Fruit |
Price |
| Mangoes |
4 kg for $12 |
| Kiwis |
6 kg for $9 |
- Ryan bought an equal mass of mangoes and kiwis and spent $90 more on mangoes than on kiwis. What was the total mass of fruits that Ryan bought?
- Shiyun spent an equal amount of money on mangoes and kiwis. In terms of their masses, what was the ratio of mangoes to the ratio of kiwis Shiyun bought?
(a)
LCM of 4 and 6 = 12
One set = 12 kg of mangoes and 12 kg of kiwis
Number of sets of 4 kg of mangoes
= 12 ÷ 4
= 3
Number of sets of 6 kg of kiwis
= 12 ÷ 6
= 2
Difference in price of mangoes and kiwis in one set
= 3 x 12 - 2 x 9
= 36 - 18
= $18
Number of sets
= 90 ÷ 18
= 5
Mass of mangoes and kiwis in one set
= 12 + 12
= 24 kg
Total mass of fruits bought
= 5 x 24
= 120 kg
(b)
LCM of 12 and 9 = 36
Number of sets of 4 kg of mangoes to be bought with $36
= 36 ÷ 12
= 3
Mass of 3 sets of 4 kg of mangoes
= 3 x 4
= 12 kg
Number of sets of 6 kg of mangoes to be bought with $36
= 36 ÷ 9
= 4
Mass of 4 sets of 6 kg of kiwis
= 4 x 6
= 24 kg
Mass of mangoes : Mass of kiwis
12 : 24
(÷12) 1 : 2
Answer(s): (a) 120 kg; (b) 1 : 2
