The ratio of the number of hens in Farm X to the number of hens in Farm Y was 7 : 9. There were 68 fewer hens in Farm X than in Farm Y. When 9 hens escaped from Farm Y, the farmer in Farm Y bought another 17 hens. What was the new ratio of the number of hens in Farm X to the number of hens in Farm Y in the end? Give your answer in the simplest form.
| |
Farm X |
Farm Y |
| Before |
7 u |
9 u |
| Change 1 |
|
- 9 |
| Change 2 |
|
+ 17 |
| After |
7 u |
9 u + 8 |
Number of fewer hens in Farm X than Farm Y
= 9 u - 7 u
= 2 u
2 u = 68
1 u = 68 ÷ 2 = 34
Number of hens in Farm X
= 7 u
= 34 x 7
= 238
Number of hens in Farm Y
= 9 u
= 34 x 9
= 306
New number of hens in Farm Y
= 9 u + 8
= 306 + 8
= 314
Farm X : Farm Y
238 : 314
(÷ 2)119 : 157
Answer(s): 119 : 157
