The prices of two fruits sold at a supermarket is shown.
| Fruit |
Price |
| Peaches |
6 kg for $14 |
| Grapefruits |
5 kg for $10 |
- Tom bought an equal mass of peaches and grapefruits and spent $70 more on peaches than on grapefruits. What was the total mass of fruits that Tom bought?
- Cathy spent an equal amount of money on peaches and grapefruits. In terms of their masses, what was the ratio of peaches to the ratio of grapefruits Cathy bought?
(a)
LCM of 6 and 5 = 30
One set = 30 kg of peaches and 30 kg of grapefruits
Number of sets of 6 kg of peaches
= 30 ÷ 6
= 5
Number of sets of 5 kg of grapefruits
= 30 ÷ 5
= 6
Difference in price of peaches and grapefruits in one set
= 5 x 14 - 6 x 10
= 70 - 60
= $10
Number of sets
= 70 ÷ 10
= 7
Mass of peaches and grapefruits in one set
= 30 + 30
= 60 kg
Total mass of fruits bought
= 7 x 60
= 420 kg
(b)
LCM of 14 and 10 = 70
Number of sets of 6 kg of peaches to be bought with $70
= 70 ÷ 14
= 5
Mass of 5 sets of 6 kg of peaches
= 5 x 6
= 30 kg
Number of sets of 5 kg of peaches to be bought with $70
= 70 ÷ 10
= 7
Mass of 7 sets of 5 kg of grapefruits
= 7 x 5
= 35 kg
Mass of peaches : Mass of grapefruits
30 : 35
(÷5) 6 : 7
Answer(s): (a) 420 kg; (b) 6 : 7
