The prices of two fruits sold at a supermarket is shown.
Fruit |
Price |
Mangosteens |
6 kg for $12 |
Dragonfruits |
5 kg for $8 |
- Howard bought an equal mass of mangosteens and dragonfruits and spent $84 more on mangosteens than on dragonfruits. What was the total mass of fruits that Howard bought?
- Kimberly spent an equal amount of money on mangosteens and dragonfruits. In terms of their masses, what was the ratio of mangosteens to the ratio of dragonfruits Kimberly bought?
(a)
LCM of 6 and 5 = 30
One set = 30 kg of mangosteens and 30 kg of dragonfruits
Number of sets of 6 kg of mangosteens
= 30 ÷ 6
= 5
Number of sets of 5 kg of dragonfruits
= 30 ÷ 5
= 6
Difference in price of mangosteens and dragonfruits in one set
= 5 x 12 - 6 x 8
= 60 - 48
= $12
Number of sets
= 84 ÷ 12
= 7
Mass of mangosteens and dragonfruits in one set
= 30 + 30
= 60 kg
Total mass of fruits bought
= 7 x 60
= 420 kg
(b)
LCM of 12 and 8 = 24
Number of sets of 6 kg of mangosteens to be bought with $24
= 24 ÷ 12
= 2
Mass of 2 sets of 6 kg of mangosteens
= 2 x 6
= 12 kg
Number of sets of 5 kg of mangosteens to be bought with $24
= 24 ÷ 8
= 3
Mass of 3 sets of 5 kg of dragonfruits
= 3 x 5
= 15 kg
Mass of mangosteens : Mass of dragonfruits
12 : 15
(÷3) 4 : 5
Answer(s): (a) 420 kg; (b) 4 : 5