Jeremy has a carton containing some bunches of green grapes and bunches of purple grapes. If he adds in 18 bunches of green grapes, 0.7 of the bunches of grapes in the carton will be bunches of purple grapes. If he adds in 54 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 - 18 |
3 p - 54 |
1 p |
Change |
|
+ 18 |
+ 54 |
|
After |
7 u |
3 u |
3 p |
1 p |
0.7 =
710 =
710If he adds 18 bunches of green grapes,
Number of bunches of green grapes in the end
= 10 u - 7 u
= 3 u
If he adds 54 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 - 54 --- (1)
3 u - 18 = 1 p
3 u = 1 p + 18 --- (2)
Make u the same.
(1)
x3 21 u = 9 p - 162 --- (3)
(2)
x7 21 u = 7 p + 126 --- (4)
(3) = (4)
9 p - 162 = 7 p + 126
9 p - 7 p = 162 + 126
2 p = 288
1 p = 288 ÷ 2 = 144
Number of bunches of grapes at first
= 1 p + 3 p - 54
= 4 p - 54
= 4 x 144 - 54
= 576 - 54
= 522
Answer(s): 522