Jeremy has a carton containing some golden kiwis and green kiwis. If he adds in 45 golden kiwis, 0.7 of the kiwis in the carton will be green kiwis. If he adds in 49 green kiwis,
34 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 |
7 u |
3 u - 45 |
3 p - 49 |
1 p |
Change |
|
+ 45 |
+ 49 |
|
After |
7 u |
3 u |
3 p |
1 p |
0.7 =
710 =
710If he adds 45 golden kiwis,
Number of golden kiwis in the end
= 10 u - 7 u
= 3 u
If he adds 49 green kiwis,
Number of golden kiwis in the end
= 4 p - 3 p
= 1 p
The number of each type in both scenarios remain unchanged at first.
7 u = 3 p - 49 --- (1)
3 u - 45 = 1 p
3 u = 1 p + 45 --- (2)
Make u the same.
(1)
x3 21 u = 9 p - 147 --- (3)
(2)
x7 21 u = 7 p + 315 --- (4)
(3) = (4)
9 p - 147 = 7 p + 315
9 p - 7 p = 147 + 315
2 p = 462
1 p = 462 ÷ 2 = 231
Number of kiwis at first
= 1 p + 3 p - 49
= 4 p - 49
= 4 x 231 - 49
= 924 - 49
= 875
Answer(s): 875