Jeremy has a carton containing some bunches of green grapes and bunches of purple grapes. If he adds in 49 bunches of green grapes, 0.7 of the bunches of grapes in the carton will be bunches of purple grapes. If he adds in 65 bunches of purple grapes,
34 of the bunches of grapes in the carton will be green bunches of grapes. How many bunches of grapes are there in the carton?
|
Bunches of purple grapes |
Bunches of green grapes |
Bunches of purple grapes |
Bunches of green grapes |
Before |
7 u |
3 u - 49 |
3 p - 65 |
1 p |
Change |
|
+ 49 |
+ 65 |
|
After |
7 u |
3 u |
3 p |
1 p |
0.7 =
710 =
710If he adds 49 bunches of green grapes,
Number of bunches of green grapes in the end
= 10 u - 7 u
= 3 u
If he adds 65 bunches of purple grapes,
Number of bunches of green grapes 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 - 65 --- (1)
3 u - 49 = 1 p
3 u = 1 p + 49 --- (2)
Make u the same.
(1)
x3 21 u = 9 p - 195 --- (3)
(2)
x7 21 u = 7 p + 343 --- (4)
(3) = (4)
9 p - 195 = 7 p + 343
9 p - 7 p = 195 + 343
2 p = 538
1 p = 538 ÷ 2 = 269
Number of bunches of grapes at first
= 1 p + 3 p - 65
= 4 p - 65
= 4 x 269 - 65
= 1076 - 65
= 1011
Answer(s): 1011