The prices of two fruits sold at a supermarket is shown.
Fruit |
Price |
Kiwis |
4 kg for $8 |
Lemons |
3 kg for $3 |
- Zane bought an equal mass of kiwis and lemons and spent $84 more on kiwis than on lemons. What was the total mass of fruits that Zane bought?
- Penelope spent an equal amount of money on kiwis and lemons. In terms of their masses, what was the ratio of kiwis to the ratio of lemons Penelope bought?
(a)
LCM of 4 and 3 = 12
One set = 12 kg of kiwis and 12 kg of lemons
Number of sets of 4 kg of kiwis
= 12 ÷ 4
= 3
Number of sets of 3 kg of lemons
= 12 ÷ 3
= 4
Difference in price of kiwis and lemons in one set
= 3 x 8 - 4 x 3
= 24 - 12
= $12
Number of sets
= 84 ÷ 12
= 7
Mass of kiwis and lemons in one set
= 12 + 12
= 24 kg
Total mass of fruits bought
= 7 x 24
= 168 kg
(b)
LCM of 8 and 3 = 24
Number of sets of 4 kg of kiwis to be bought with $24
= 24 ÷ 8
= 3
Mass of 3 sets of 4 kg of kiwis
= 3 x 4
= 12 kg
Number of sets of 3 kg of kiwis to be bought with $24
= 24 ÷ 3
= 8
Mass of 8 sets of 3 kg of lemons
= 8 x 3
= 24 kg
Mass of kiwis : Mass of lemons
12 : 24
(÷12) 1 : 2
Answer(s): (a) 168 kg; (b) 1 : 2