The ratio of the number of ducks in Farm P to the number of ducks in Farm Q was 3 : 5. There were 68 fewer ducks in Farm P than in Farm Q. When 6 ducks escaped from Farm Q, the farmer in Farm Q bought another 13 ducks. What was the new ratio of the number of ducks in Farm P to the number of ducks in Farm Q in the end? Give your answer in the simplest form.
| |
Farm P |
Farm Q |
| Before |
3 u |
5 u |
| Change 1 |
|
- 6 |
| Change 2 |
|
+ 13 |
| After |
3 u |
5 u + 7 |
Number of fewer ducks in Farm P than Farm Q
= 5 u - 3 u
= 2 u
2 u = 68
1 u = 68 ÷ 2 = 34
Number of ducks in Farm P
= 3 u
= 34 x 3
= 102
Number of ducks in Farm Q
= 5 u
= 34 x 5
= 170
New number of ducks in Farm Q
= 5 u + 7
= 170 + 7
= 177
Farm P : Farm Q
102 : 177
(÷ 3)34 : 59
Answer(s): 34 : 59
