14 of the number of ducks that Farmer Sean had was equal to
34 of the number of ducks that Farmer Ben had. When Farmer Sean sold 300 of his ducks and Farmer Ben bought another 40, the ratio of the number of ducks that Farmer Sean had to the number of ducks Farmer Ben had become 4 : 3. What was the total number of ducks that the 2 farmers had at first?
|
Make p the same (1) x 3 = (3) |
Farmer Sean (1) |
Farmer Ben (2) |
Make p the same (2) x 4 = (4) |
Before |
36 u |
12 u |
4 u |
16 u |
Change |
- 900 |
- 300 |
+ 40 |
+ 160 |
After |
12 p |
4 p |
3 p |
12 p |
Make the numerators the same.
1x34x3 Farmer Sean's ducks =
3x14x1 Farmer Ben's ducks
312 Farmer Sean's ducks =
34 Farmer Ben's ducks
36 u - 900 = 16 u + 160
36 u - 16 u = 160 + 900
20 u = 1060
1 u = 1060 ÷ 20 = 53
Total number of ducks that the 2 farmers had
= 12 u + 4 u
= 16 u
= 16 x 53
= 848
Answer(s): 848