Kylie had four boxes, B, C, D and E which contained a total of 220 apples. She transferred 15 apples from Box B to Box C, 36 apples from Box C to Box D and 52 apples from Box D to Box E. The ratio of the number of apples in Box B to Box C to Box D changed from 3 : 6 : 11 to 1 : 3 : 8. How many apples were in Box E at first?
| |
Make p the same
(1)x3 = (3) |
B
(1) |
C
(2) |
D
|
E
|
| Before |
9 u |
3 u |
6 u |
11 u |
? |
| Change 1 |
- 45 |
- 15 |
+ 15 |
|
|
| Change 2 |
|
|
- 36 |
+ 36 |
|
| Change 3 |
|
|
|
- 52 |
+ 52 |
| After |
3 p |
1 p |
3 p |
8 p |
? |
3 u - 15 = 1 p --- (1)
6 u + 15 - 36 = 3 p
6 u - 21 =
3 p --- (2)
(1)
x 3 9 u - 45 =
3 p --- (3)
Make p the same.
(3) = (2)
9 u - 45 = 6 u - 21
9 u - 6 u = 45 - 21
3 u = 24
1 u = 24 ÷ 3 = 8
Total number of apples in Box B, Box C and Box D
= 3 u + 6 u + 11 u
= 20 u
Total number of apples in Box E at first
= 220 - 20 u
= 220 - 20 x 8
= 220 - 160
= 60
Answer(s): 60
