Jeremy has a carton containing some golden kiwis and green kiwis. If he adds in 23 golden kiwis, 0.6 of the kiwis in the carton will be green kiwis. If he adds in 48 green kiwis,
45 of the kiwis in the carton will be green kiwis. How many kiwis are there in the carton?
|
Green kiwis |
Golden kiwis |
Green kiwis |
Golden kiwis |
Before |
3 u |
2 u - 23 |
4 p - 48 |
1 p |
Change |
|
+ 23 |
+ 48 |
|
After |
3 u |
2 u |
4 p |
1 p |
0.6 =
610 =
35If he adds 23 golden kiwis,
Number of golden kiwis in the end
= 5 u - 3 u
= 2 u
If he adds 48 green kiwis,
Number of golden kiwis in the end
= 5 p - 4 p
= 1 p
The number of each type in both scenarios remain unchanged at first.
3 u = 4 p - 48 --- (1)
2 u - 23 = 1 p
2 u = 1 p + 23 --- (2)
Make u the same.
(1)
x2 6 u = 8 p - 96 --- (3)
(2)
x3 6 u = 3 p + 69 --- (4)
(3) = (4)
8 p - 96 = 3 p + 69
8 p - 3 p = 96 + 69
5 p = 165
1 p = 165 ÷ 5 = 33
Number of kiwis at first
= 1 p + 4 p - 48
= 5 p - 48
= 5 x 33 - 48
= 165 - 48
= 117
Answer(s): 117