Jeremy has a carton containing some fuji apples and washington apples. If he adds in 27 fuji apples, 0.6 of the apples in the carton will be washington apples. If he adds in 42 washington apples,
78 of the apples in the carton will be green apples. How many apples are there in the carton?
|
Washington apples |
Fuji apples |
Washington apples |
Fuji apples |
Before |
3 u |
2 u - 27 |
7 p - 42 |
1 p |
Change |
|
+ 27 |
+ 42 |
|
After |
3 u |
2 u |
7 p |
1 p |
0.6 =
610 =
35If he adds 27 fuji apples,
Number of fuji apples in the end
= 5 u - 3 u
= 2 u
If he adds 42 washington apples,
Number of fuji apples in the end
= 8 p - 7 p
= 1 p
The number of each type in both scenarios remain unchanged at first.
3 u = 7 p - 42 --- (1)
2 u - 27 = 1 p
2 u = 1 p + 27 --- (2)
Make u the same.
(1)
x2 6 u = 14 p - 84 --- (3)
(2)
x3 6 u = 3 p + 81 --- (4)
(3) = (4)
14 p - 84 = 3 p + 81
14 p - 3 p = 84 + 81
11 p = 165
1 p = 165 ÷ 11 = 15
Number of apples at first
= 1 p + 7 p - 42
= 8 p - 42
= 8 x 15 - 42
= 120 - 42
= 78
Answer(s): 78