Jeremy has a carton containing some fuji apples and washington apples. If he adds in 28 fuji apples, 0.7 of the apples in the carton will be washington apples. If he adds in 50 washington apples,
34 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 |
7 u |
3 u - 28 |
3 p - 50 |
1 p |
Change |
|
+ 28 |
+ 50 |
|
After |
7 u |
3 u |
3 p |
1 p |
0.7 =
710 =
710If he adds 28 fuji apples,
Number of fuji apples in the end
= 10 u - 7 u
= 3 u
If he adds 50 washington apples,
Number of fuji apples 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 - 50 --- (1)
3 u - 28 = 1 p
3 u = 1 p + 28 --- (2)
Make u the same.
(1)
x3 21 u = 9 p - 150 --- (3)
(2)
x7 21 u = 7 p + 196 --- (4)
(3) = (4)
9 p - 150 = 7 p + 196
9 p - 7 p = 150 + 196
2 p = 346
1 p = 346 ÷ 2 = 173
Number of apples at first
= 1 p + 3 p - 50
= 4 p - 50
= 4 x 173 - 50
= 692 - 50
= 642
Answer(s): 642