13 of the number of ducks that Farmer John had was equal to
34 of the number of ducks that Farmer Andy had. When Farmer John sold 300 of his ducks and Farmer Andy bought another 40, the ratio of the number of ducks that Farmer John had to the number of ducks Farmer Andy had become 6 : 7. What was the total number of ducks that the 2 farmers had at first?
|
Make p the same (1) x 7 = (3) |
Farmer John (1) |
Farmer Andy (2) |
Make p the same (2) x 6 = (4) |
Before |
63 u |
9 u |
4 u |
24 u |
Change |
- 2100 |
- 300 |
+ 40 |
+ 240 |
After |
42 p |
6 p |
7 p |
42 p |
Make the numerators the same.
1x33x3 Farmer John's ducks =
3x14x1 Farmer Andy's ducks
39 Farmer John's ducks =
34 Farmer Andy's ducks
63 u - 2100 = 24 u + 240
63 u - 24 u = 240 + 2100
39 u = 2340
1 u = 2340 ÷ 39 = 60
Total number of ducks that the 2 farmers had
= 9 u + 4 u
= 13 u
= 13 x 60
= 780
Answer(s): 780