Question

The number of chickens to the number of ducks on a farm was 6:5. After 63 ducks were sold, there were 3 times as many chickens as ducks left.

Answer 1

To solve this problem, we can set up a system of equations and solve them simultaneously. The number of ducks on the farm is 95, and the number of chickens is 114.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's say the number of chickens is represented by x and the number of ducks is represented by y. From the given information, we can write the following equations:

x/y = 6/5

x - 63 = 3(y - 63)

We can solve these equations simultaneously to find the values of x and y. First, we can cross-multiply the first equation to get 5x = 6y. Then, we can substitute this expression for x in the second equation: 5y - 63 = 3(y - 63). Simplifying the equation, we get 2y = 189. Finally, we can solve for y: y = 189/2 = 94.5. Since the number of chickens and ducks must be whole numbers, we know that there must be 95 ducks on the farm. To find the number of chickens, we can substitute this value into the first equation: x/95 = 6/5. Cross-multiplying, we get 5x = 6 * 95 = 570. Solving for x, we find that there are 570/5 = 114 chickens on the farm.

Answer 2

c:d=6:5
63 ducks sold
then the ratio is not
3:1
so
3:1 times 2:2=6:2
so from 6:5 then 63 weere sold becomes 6:2
therefor 3 duck units=63
therefor
3/63=1/21
1 unit=21
there is not question so I will solve for
1. total number
2. original numbe rof chickens
3. original number of ducks
4. final numbe rofo ducks


total number=total units times number per unit
number per unit=21
ttoal units=5+6=11
21 times 11=231

total=231


chickens=6 units
6 times 11=126


original ducks=5 units
5 times 21=105

resulting number of ducks
2 units
2 times 21=42





total=231
original chickens=126
original ducks=105
final number of ducks=42