The prices of two fruits sold at a supermarket is shown.
Fruit |
Price |
Pomegranates |
6 kg for $13 |
Guavas |
8 kg for $8 |
- Warren bought an equal mass of pomegranates and guavas and spent $84 more on pomegranates than on guavas. What was the total mass of fruits that Warren bought?
- Barbara spent an equal amount of money on pomegranates and guavas. In terms of their masses, what was the ratio of pomegranates to the ratio of guavas Barbara bought?
(a)
LCM of 6 and 8 = 24
One set = 24 kg of pomegranates and 24 kg of guavas
Number of sets of 6 kg of pomegranates
= 24 ÷ 6
= 4
Number of sets of 8 kg of guavas
= 24 ÷ 8
= 3
Difference in price of pomegranates and guavas in one set
= 4 x 13 - 3 x 8
= 52 - 24
= $28
Number of sets
= 84 ÷ 28
= 3
Mass of pomegranates and guavas in one set
= 24 + 24
= 48 kg
Total mass of fruits bought
= 3 x 48
= 144 kg
(b)
LCM of 13 and 8 = 104
Number of sets of 6 kg of pomegranates to be bought with $104
= 104 ÷ 13
= 8
Mass of 8 sets of 6 kg of pomegranates
= 8 x 6
= 48 kg
Number of sets of 8 kg of pomegranates to be bought with $104
= 104 ÷ 8
= 13
Mass of 13 sets of 8 kg of guavas
= 13 x 8
= 104 kg
Mass of pomegranates : Mass of guavas
48 : 104
(÷8) 6 : 13
Answer(s): (a) 144 kg; (b) 6 : 13