The ratio of the number of hens in Farm Y to the number of hens in Farm Z was 3 : 5. There were 66 fewer hens in Farm Y than in Farm Z. When 12 hens escaped from Farm Z, the farmer in Farm Z bought another 18 hens. What was the new ratio of the number of hens in Farm Y to the number of hens in Farm Z in the end? Give your answer in the simplest form.
| |
Farm Y |
Farm Z |
| Before |
3 u |
5 u |
| Change 1 |
|
- 12 |
| Change 2 |
|
+ 18 |
| After |
3 u |
5 u + 6 |
Number of fewer hens in Farm Y than Farm Z
= 5 u - 3 u
= 2 u
2 u = 66
1 u = 66 ÷ 2 = 33
Number of hens in Farm Y
= 3 u
= 33 x 3
= 99
Number of hens in Farm Z
= 5 u
= 33 x 5
= 165
New number of hens in Farm Z
= 5 u + 6
= 165 + 6
= 171
Farm Y : Farm Z
99 : 171
(÷ 9)11 : 19
Answer(s): 11 : 19
