The prices of two fruits sold at a supermarket is shown.
| Fruit |
Price |
| Pears |
3 kg for $11 |
| Pomegranates |
6 kg for $4 |
- Ben bought an equal mass of pears and pomegranates and spent $90 more on pears than on pomegranates. What was the total mass of fruits that Ben bought?
- Dana spent an equal amount of money on pears and pomegranates. In terms of their masses, what was the ratio of pears to the ratio of pomegranates Dana bought?
(a)
LCM of 3 and 6 = 6
One set = 6 kg of pears and 6 kg of pomegranates
Number of sets of 3 kg of pears
= 6 ÷ 3
= 2
Number of sets of 6 kg of pomegranates
= 6 ÷ 6
= 1
Difference in price of pears and pomegranates in one set
= 2 x 11 - 1 x 4
= 22 - 4
= $18
Number of sets
= 90 ÷ 18
= 5
Mass of pears and pomegranates in one set
= 6 + 6
= 12 kg
Total mass of fruits bought
= 5 x 12
= 60 kg
(b)
LCM of 11 and 4 = 44
Number of sets of 3 kg of pears to be bought with $44
= 44 ÷ 11
= 4
Mass of 4 sets of 3 kg of pears
= 4 x 3
= 12 kg
Number of sets of 6 kg of pears to be bought with $44
= 44 ÷ 4
= 11
Mass of 11 sets of 6 kg of pomegranates
= 11 x 6
= 66 kg
Mass of pears : Mass of pomegranates
12 : 66
(÷6) 2 : 11
Answer(s): (a) 60 kg; (b) 2 : 11
