Jeremy has a carton containing some bunches of purple grapes and bunches of green grapes. If he adds in 44 bunches of purple grapes, 0.7 of the bunches of grapes in the carton will be bunches of green grapes. If he adds in 58 bunches of green 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 green grapes |
Bunches of purple grapes |
Bunches of green grapes |
Bunches of purple grapes |
Before |
7 u |
3 u - 44 |
3 p - 58 |
1 p |
Change |
|
+ 44 |
+ 58 |
|
After |
7 u |
3 u |
3 p |
1 p |
0.7 =
710 =
710If he adds 44 bunches of purple grapes,
Number of bunches of purple grapes in the end
= 10 u - 7 u
= 3 u
If he adds 58 bunches of green grapes,
Number of bunches of purple 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 - 58 --- (1)
3 u - 44 = 1 p
3 u = 1 p + 44 --- (2)
Make u the same.
(1)
x3 21 u = 9 p - 174 --- (3)
(2)
x7 21 u = 7 p + 308 --- (4)
(3) = (4)
9 p - 174 = 7 p + 308
9 p - 7 p = 174 + 308
2 p = 482
1 p = 482 ÷ 2 = 241
Number of bunches of grapes at first
= 1 p + 3 p - 58
= 4 p - 58
= 4 x 241 - 58
= 964 - 58
= 906
Answer(s): 906