The prices of two fruits sold at a supermarket is shown.
| Fruit |
Price |
| Kiwis |
5 kg for $11 |
| Guavas |
8 kg for $10 |
- Will bought an equal mass of kiwis and guavas and spent $114 more on kiwis than on guavas. What was the total mass of fruits that Will bought?
- Cathy spent an equal amount of money on kiwis and guavas. In terms of their masses, what was the ratio of kiwis to the ratio of guavas Cathy bought?
(a)
LCM of 5 and 8 = 40
One set = 40 kg of kiwis and 40 kg of guavas
Number of sets of 5 kg of kiwis
= 40 ÷ 5
= 8
Number of sets of 8 kg of guavas
= 40 ÷ 8
= 5
Difference in price of kiwis and guavas in one set
= 8 x 11 - 5 x 10
= 88 - 50
= $38
Number of sets
= 114 ÷ 38
= 3
Mass of kiwis and guavas in one set
= 40 + 40
= 80 kg
Total mass of fruits bought
= 3 x 80
= 240 kg
(b)
LCM of 11 and 10 = 110
Number of sets of 5 kg of kiwis to be bought with $110
= 110 ÷ 11
= 10
Mass of 10 sets of 5 kg of kiwis
= 10 x 5
= 50 kg
Number of sets of 8 kg of kiwis to be bought with $110
= 110 ÷ 10
= 11
Mass of 11 sets of 8 kg of guavas
= 11 x 8
= 88 kg
Mass of kiwis : Mass of guavas
50 : 88
(÷2) 25 : 44
Answer(s): (a) 240 kg; (b) 25 : 44
