The ratio of the number of ducks in Farm E to the number of ducks in Farm F was 5 : 8. There were 54 fewer ducks in Farm E than in Farm F. When 5 ducks escaped from Farm F, the farmer in Farm F bought another 15 ducks. What was the new ratio of the number of ducks in Farm E to the number of ducks in Farm F in the end? Give your answer in the simplest form.
| |
Farm E |
Farm F |
| Before |
5 u |
8 u |
| Change 1 |
|
- 5 |
| Change 2 |
|
+ 15 |
| After |
5 u |
8 u + 10 |
Number of fewer ducks in Farm E than Farm F
= 8 u - 5 u
= 3 u
3 u = 54
1 u = 54 ÷ 3 = 18
Number of ducks in Farm E
= 5 u
= 18 x 5
= 90
Number of ducks in Farm F
= 8 u
= 18 x 8
= 144
New number of ducks in Farm F
= 8 u + 10
= 144 + 10
= 154
Farm E : Farm F
90 : 154
(÷ 2)45 : 77
Answer(s): 45 : 77
