On a small farm, there are 3 times as many ducks as horses. Between them there are 160 legs. How many horses are there?

Let's denote the number of horses as \( h \), and the number of ducks as \( d \).

We are given two key pieces of information:

1. There are 3 times as many ducks as horses, which gives us the equation:
   \[
   d = 3h
   \]

2. Between the ducks and horses, there are 160 legs. Since each horse has 4 legs and each duck has 2 legs, we can express the total number of legs as:
   \[
   4h + 2d = 160
   \]

Now, substitute the expression \( d = 3h \) into the legs equation:
\[
4h + 2(3h) = 160
\]

Simplify the equation:
\[
4h + 6h = 160
\]
\[
10h = 160
\]

Now, solve for \( h \):
\[
h = \frac{160}{10} = 16
\]

Thus, there are 16 horses on the farm.

If you want to check, the number of ducks is \( 3 \times 16 = 48 \). The total number of legs is:
\[
4 \times 16 + 2 \times 48 = 64 + 96 = 160
\]
which matches the given information.

### Conclusion:
There are 16 horses on the farm.

Would you like more details or have any other questions?

### Related Questions:
1. How many ducks are there on the farm?
2. If the number of ducks doubled, how many legs would there be?
3. What if there were 4 times as many ducks as horses, how would the equation change?
4. If the number of legs was 200 instead of 160, how many horses would there be?
5. Can you create an equation for the number of legs if ducks have 3 legs instead?

### Tip:
When solving word problems, always translate the words into algebraic expressions to find the relationship between different quantities.

Discover how to solve an algebra word problem involving horses and ducks on a farm. Learn how to set up and solve linear equations using the given data, including how to calculate the number of horses and ducks based on the total number of legs. Suitable for students in Grades 6-8.

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