The prices of two fruits sold at a supermarket is shown.
| Fruit |
Price |
| Peaches |
2 kg for $7 |
| Mangoes |
6 kg for $9 |
- Cole bought an equal mass of peaches and mangoes and spent $48 more on peaches than on mangoes. What was the total mass of fruits that Cole bought?
- Gwen spent an equal amount of money on peaches and mangoes. In terms of their masses, what was the ratio of peaches to the ratio of mangoes Gwen bought?
(a)
LCM of 2 and 6 = 6
One set = 6 kg of peaches and 6 kg of mangoes
Number of sets of 2 kg of peaches
= 6 ÷ 2
= 3
Number of sets of 6 kg of mangoes
= 6 ÷ 6
= 1
Difference in price of peaches and mangoes in one set
= 3 x 7 - 1 x 9
= 21 - 9
= $12
Number of sets
= 48 ÷ 12
= 4
Mass of peaches and mangoes in one set
= 6 + 6
= 12 kg
Total mass of fruits bought
= 4 x 12
= 48 kg
(b)
LCM of 7 and 9 = 63
Number of sets of 2 kg of peaches to be bought with $63
= 63 ÷ 7
= 9
Mass of 9 sets of 2 kg of peaches
= 9 x 2
= 18 kg
Number of sets of 6 kg of peaches to be bought with $63
= 63 ÷ 9
= 7
Mass of 7 sets of 6 kg of mangoes
= 7 x 6
= 42 kg
Mass of peaches : Mass of mangoes
18 : 42
(÷6) 3 : 7
Answer(s): (a) 48 kg; (b) 3 : 7
