14 of the number of ducks that Farmer Jack had was equal to
34 of the number of ducks that Farmer Luis had. When Farmer Jack sold 300 of his ducks and Farmer Luis bought another 40, the ratio of the number of ducks that Farmer Jack had to the number of ducks Farmer Luis had become 2 : 3. What was the total number of ducks that the 2 farmers had at first?
|
Make p the same (1) x 3 = (3) |
Farmer Jack (1) |
Farmer Luis (2) |
Make p the same (2) x 2 = (4) |
Before |
36 u |
12 u |
4 u |
8 u |
Change |
- 900 |
- 300 |
+ 40 |
+ 80 |
After |
6 p |
2 p |
3 p |
6 p |
Make the numerators the same.
1x34x3 Farmer Jack's ducks =
3x14x1 Farmer Luis's ducks
312 Farmer Jack's ducks =
34 Farmer Luis's ducks
36 u - 900 = 8 u + 80
36 u - 8 u = 80 + 900
28 u = 980
1 u = 980 ÷ 28 = 35
Total number of ducks that the 2 farmers had
= 12 u + 4 u
= 16 u
= 16 x 35
= 560
Answer(s): 560