The prices of two fruits sold at a supermarket is shown.
Fruit |
Price |
Pears |
3 kg for $7 |
Lemons |
6 kg for $5 |
- Reggie bought an equal mass of pears and lemons and spent $27 more on pears than on lemons. What was the total mass of fruits that Reggie bought?
- Natalie spent an equal amount of money on pears and lemons. In terms of their masses, what was the ratio of pears to the ratio of lemons Natalie bought?
(a)
LCM of 3 and 6 = 6
One set = 6 kg of pears and 6 kg of lemons
Number of sets of 3 kg of pears
= 6 ÷ 3
= 2
Number of sets of 6 kg of lemons
= 6 ÷ 6
= 1
Difference in price of pears and lemons in one set
= 2 x 7 - 1 x 5
= 14 - 5
= $9
Number of sets
= 27 ÷ 9
= 3
Mass of pears and lemons in one set
= 6 + 6
= 12 kg
Total mass of fruits bought
= 3 x 12
= 36 kg
(b)
LCM of 7 and 5 = 35
Number of sets of 3 kg of pears to be bought with $35
= 35 ÷ 7
= 5
Mass of 5 sets of 3 kg of pears
= 5 x 3
= 15 kg
Number of sets of 6 kg of pears to be bought with $35
= 35 ÷ 5
= 7
Mass of 7 sets of 6 kg of lemons
= 7 x 6
= 42 kg
Mass of pears : Mass of lemons
15 : 42
(÷3) 5 : 14
Answer(s): (a) 36 kg; (b) 5 : 14