The ratio of the number of hens in Farm Z to the number of hens in Farm A was 7 : 10. There were 66 fewer hens in Farm Z than in Farm A. When 9 hens escaped from Farm A, the farmer in Farm A bought another 19 hens. What was the new ratio of the number of hens in Farm Z to the number of hens in Farm A in the end? Give your answer in the simplest form.
| |
Farm Z |
Farm A |
| Before |
7 u |
10 u |
| Change 1 |
|
- 9 |
| Change 2 |
|
+ 19 |
| After |
7 u |
10 u + 10 |
Number of fewer hens in Farm Z than Farm A
= 10 u - 7 u
= 3 u
3 u = 66
1 u = 66 ÷ 3 = 22
Number of hens in Farm Z
= 7 u
= 22 x 7
= 154
Number of hens in Farm A
= 10 u
= 22 x 10
= 220
New number of hens in Farm A
= 10 u + 10
= 220 + 10
= 230
Farm Z : Farm A
154 : 230
(÷ 2)77 : 115
Answer(s): 77 : 115
