14 of the number of ducks that Farmer Caden had was equal to
35 of the number of ducks that Farmer Tom had. When Farmer Caden sold 300 of his ducks and Farmer Tom bought another 40, the ratio of the number of ducks that Farmer Caden had to the number of ducks Farmer Tom had become 3 : 2. What was the total number of ducks that the 2 farmers had at first?
|
Make p the same (1) x 2 = (3) |
Farmer Caden (1) |
Farmer Tom (2) |
Make p the same (2) x 3 = (4) |
Before |
24 u |
12 u |
5 u |
15 u |
Change |
- 600 |
- 300 |
+ 40 |
+ 120 |
After |
6 p |
3 p |
2 p |
6 p |
Make the numerators the same.
1x34x3 Farmer Caden's ducks =
3x15x1 Farmer Tom's ducks
312 Farmer Caden's ducks =
35 Farmer Tom's ducks
24 u - 600 = 15 u + 120
24 u - 15 u = 120 + 600
9 u = 720
1 u = 720 ÷ 9 = 80
Total number of ducks that the 2 farmers had
= 12 u + 5 u
= 17 u
= 17 x 80
= 1360
Answer(s): 1360