13 of the number of ducks that Farmer Oliver had was equal to
34 of the number of ducks that Farmer Caden had. When Farmer Oliver sold 300 of his ducks and Farmer Caden bought another 40, the ratio of the number of ducks that Farmer Oliver had to the number of ducks Farmer Caden 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 Oliver (1) |
Farmer Caden (2) |
Make p the same (2) x 3 = (4) |
Before |
18 u |
9 u |
4 u |
12 u |
Change |
- 600 |
- 300 |
+ 40 |
+ 120 |
After |
6 p |
3 p |
2 p |
6 p |
Make the numerators the same.
1x33x3 Farmer Oliver's ducks =
3x14x1 Farmer Caden's ducks
39 Farmer Oliver's ducks =
34 Farmer Caden's ducks
18 u - 600 = 12 u + 120
18 u - 12 u = 120 + 600
6 u = 720
1 u = 720 ÷ 6 = 120
Total number of ducks that the 2 farmers had
= 9 u + 4 u
= 13 u
= 13 x 120
= 1560
Answer(s): 1560