Jenson 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 apples was 1 : 6. When he reached Shop T, he unloaded
78 of the apples and some pomegranates from his vehicle. The ratio of pomegranates to apples became 2 : 3. At Shop U, 58 pomegranates and 47 apples were collected and the number of pomegranates to apples became the same.
- How many fruits were there on his vehicle after visiting Shop U?
- How many pomegranates were delivered to Shop T?
|
Location |
Pomegranates |
Apples |
Comparing pomegranates and apples at first |
Shop S |
1x4 = 4 u |
6x4 = 24 u |
Before 1 |
Shop S |
4 u |
8x3 = 24 u |
Change 1 |
Shop T |
- ? |
- 7x3 = - 21 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 apples after unloading at Shop T is repeated. Make the number of apples left after unloading at Shop T the same. LCM of 3 and 1 is 3.
The number of apples collected at Shop S is repeated. Make the number of apples collected at Shop S the same by multiplying 6 by 4.
The number of pomegranates and apples 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 vehicle after collecting from Shop U
= 2 u + 58
= 2 x 11 + 58
= 22 + 58
= 80
Number of fruits on his vehicle after collecting from Shop U
= 2 x 80
= 160
(b)
Number of pomegranates delivered to Shop T
= 4 u - 2 u
= 2 u
= 2 x 11
= 22
Answer(s): (a) 160; (b) 22