there are 19 more cows than sheep. there are 19 more ducks than hen there are more hens than cow

Question

there are 19 more cows than sheep. there are 19 more ducks than hen there are more hens than cow

Answer 1

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Answer 2

To solve this problem step-by-step, let's assign some variables:

Let's call the number of cows as "C", the number of sheep as "S", the number of ducks as "D", and the number of hens as "H".

From the given information, we can create the following equations:

1. There are 19 more cows than sheep: C = S + 19

2. There are 19 more ducks than hens: D = H + 19

3. There are more hens than cows: H > C

Now, let's solve the system of equations:

Since the number of hens (H) is greater than the number of cows (C), we can substitute H in terms of C in equation 2.

H = C + 1

Now, substitute H in terms of C in equation 2:

D = (C + 1) + 19

Simplify the equation:

D = C + 20

So, D is 20 more than C.

Now, substitute D in terms of C in equation 1:

C + 20 = S + 19

Simplify the equation:

C - S = 1

So, C is 1 more than S.

From these equations, we can conclude:

- The number of cows is 1 more than the number of sheep.
- The number of ducks is 20 more than the number of cows.
- The number of hens is 1 more than the number of cows.
- The number of cows, sheep, ducks, and hens are all different.

Please let me know if you need any further assistance.

Answer 3

To solve this problem, we can use a system of equations. Let's assign variables to represent the number of each animal:

Let's say the number of cows is represented by "c," the number of sheep by "s," the number of ducks by "d," and the number of hens by "h."

From the given information, we can write the following equations:

1) There are 19 more cows than sheep: c = s + 19

2) There are 19 more ducks than hens: d = h + 19

3) There are more hens than cows: h > c

Using these equations, we can find the values of c, s, d, and h.

We can start by substituting the value of s + 19 in place of c in equation 3:

h > s + 19

Next, we can substitute s + 19 in place of h in equation 2:

d = (s + 19) + 19

We can then substitute s + 19 in place of d in equation 1:

(s + 19) = s + 19

Now, we simplify the equation:

s + 19 = s + 19

The equation simplifies to:

19 = 19

This equation is always true, so there are infinitely many possible solutions. This means we can't determine the exact values of c, s, d, and h with the given information.

However, we can still make some general observations based on the equations:

- The number of cows and sheep must differ by 19.
- The number of ducks and hens must also differ by 19.
- The number of hens is greater than the number of cows.

These observations hold true for any combination of values that satisfy the given conditions.