Ken had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop S and the ratio of pomegranates to oranges was 5 : 6. When he reached Shop T, he unloaded
56 of the oranges and some pomegranates from his lorry. The ratio of pomegranates to oranges became 2 : 3. At Shop U, 58 pomegranates and 47 oranges were collected and the number of pomegranates to oranges became the same.
- How many fruits were there on his lorry after visiting Shop U?
- How many pomegranates were delivered to Shop T?
|
Location |
Pomegranates |
Oranges |
Comparing pomegranates and oranges at first |
Shop S |
5x3 = 15 u |
6x3 = 18 u |
Before 1 |
Shop S |
15 u |
6x3 = 18 u |
Change 1 |
Shop T |
- ? |
- 5x3 = - 15 u |
After 1 |
Shop U |
2 u |
1x3 = 3 u |
Before 2 |
Shop U |
2x1 = 2 u |
3x1 = 3 u |
Change 2 |
Shop U |
+ 58 |
+ 47 |
After 2 |
Shop U |
2 u + 58 |
3 u + 47 |
(a)
The number of oranges after unloading at Shop T is repeated. Make the number of oranges left after unloading at Shop T the same. LCM of 3 and 1 is 3.
The number of oranges collected at Shop S is repeated. Make the number of oranges collected at Shop S the same by multiplying 6 by 3.
The number of pomegranates and oranges in the end is the same.
3 u + 47 = 2 u + 58
3 u - 2 u = 58 - 47
1 u = 11
Number of pomegranates on his lorry after collecting from Shop U
= 2 u + 58
= 2 x 11 + 58
= 22 + 58
= 80
Number of fruits on his lorry after collecting from Shop U
= 2 x 80
= 160
(b)
Number of pomegranates delivered to Shop T
= 15 u - 2 u
= 13 u
= 13 x 11
= 143
Answer(s): (a) 160; (b) 143