The prices of two fruits sold at a supermarket is shown.
| Fruit |
Price |
| Peaches |
6 kg for $12 |
| Passion Fruits |
8 kg for $10 |
- Wesley bought an equal mass of peaches and passion fruits and spent $54 more on peaches than on passion fruits. What was the total mass of fruits that Wesley bought?
- Hazel spent an equal amount of money on peaches and passion fruits. In terms of their masses, what was the ratio of peaches to the ratio of passion fruits Hazel bought?
(a)
LCM of 6 and 8 = 24
One set = 24 kg of peaches and 24 kg of passion fruits
Number of sets of 6 kg of peaches
= 24 ÷ 6
= 4
Number of sets of 8 kg of passion fruits
= 24 ÷ 8
= 3
Difference in price of peaches and passion fruits in one set
= 4 x 12 - 3 x 10
= 48 - 30
= $18
Number of sets
= 54 ÷ 18
= 3
Mass of peaches and passion fruits in one set
= 24 + 24
= 48 kg
Total mass of fruits bought
= 3 x 48
= 144 kg
(b)
LCM of 12 and 10 = 60
Number of sets of 6 kg of peaches to be bought with $60
= 60 ÷ 12
= 5
Mass of 5 sets of 6 kg of peaches
= 5 x 6
= 30 kg
Number of sets of 8 kg of peaches to be bought with $60
= 60 ÷ 10
= 6
Mass of 6 sets of 8 kg of passion fruits
= 6 x 8
= 48 kg
Mass of peaches : Mass of passion fruits
30 : 48
(÷6) 5 : 8
Answer(s): (a) 144 kg; (b) 5 : 8
