The prices of two fruits sold at a supermarket is shown.
| Fruit |
Price |
| Lemons |
4 kg for $8 |
| Guavas |
6 kg for $3 |
- Luke bought an equal mass of lemons and guavas and spent $90 more on lemons than on guavas. What was the total mass of fruits that Luke bought?
- Linda spent an equal amount of money on lemons and guavas. In terms of their masses, what was the ratio of lemons to the ratio of guavas Linda bought?
(a)
LCM of 4 and 6 = 12
One set = 12 kg of lemons and 12 kg of guavas
Number of sets of 4 kg of lemons
= 12 ÷ 4
= 3
Number of sets of 6 kg of guavas
= 12 ÷ 6
= 2
Difference in price of lemons and guavas in one set
= 3 x 8 - 2 x 3
= 24 - 6
= $18
Number of sets
= 90 ÷ 18
= 5
Mass of lemons and guavas in one set
= 12 + 12
= 24 kg
Total mass of fruits bought
= 5 x 24
= 120 kg
(b)
LCM of 8 and 3 = 24
Number of sets of 4 kg of lemons to be bought with $24
= 24 ÷ 8
= 3
Mass of 3 sets of 4 kg of lemons
= 3 x 4
= 12 kg
Number of sets of 6 kg of lemons to be bought with $24
= 24 ÷ 3
= 8
Mass of 8 sets of 6 kg of guavas
= 8 x 6
= 48 kg
Mass of lemons : Mass of guavas
12 : 48
(÷12) 1 : 4
Answer(s): (a) 120 kg; (b) 1 : 4
