The ratio of the number of hens in Farm Z to the number of hens in Farm A was 3 : 5. There were 64 fewer hens in Farm Z than in Farm A. When 5 hens escaped from Farm A, the farmer in Farm A bought another 17 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 |
3 u |
5 u |
| Change 1 |
|
- 5 |
| Change 2 |
|
+ 17 |
| After |
3 u |
5 u + 12 |
Number of fewer hens in Farm Z than Farm A
= 5 u - 3 u
= 2 u
2 u = 64
1 u = 64 ÷ 2 = 32
Number of hens in Farm Z
= 3 u
= 32 x 3
= 96
Number of hens in Farm A
= 5 u
= 32 x 5
= 160
New number of hens in Farm A
= 5 u + 12
= 160 + 12
= 172
Farm Z : Farm A
96 : 172
(÷ 4)24 : 43
Answer(s): 24 : 43
