Question

A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses' back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70, how many horses are there?

• A. 14
• B. 16
• C. 18
• D. 20
• E.

Hint:

In problems involving legs and animals, break down the total legs by separating the legs of the people and animals, and use equations to solve.

Answer 1

The Correct Option is A

1. Define Variables:
Let \( h \) be the number of horses.
Since the number of men is equal to the number of horses, the number of men is also \( h \).
2. Understand the Scenario:
Half of the owners (men) are riding their horses, and the other half are walking and leading their horses.
Riding owners: \( \frac{h}{2} \) men are on their horses. These men are not walking, so their legs are not on the ground.
Walking owners: \( \frac{h}{2} \) men are walking and leading their horses. Each walking man has 2 legs on the ground.
Horses: Each horse has 4 legs. All horses are walking, so their legs are on the ground.
3. Calculate the Total Number of Legs on the Ground:
Legs from walking men:
\[ \text{Legs from walking men} = \frac{h}{2} \times 2 = h \] Legs from horses:
\[ \text{Legs from horses} = h \times 4 = 4h \] Total legs on the ground:
\[ \text{Total legs} = \text{Legs from walking men} + \text{Legs from horses} = h + 4h = 5h \] 4. Set Up the Equation:
The total number of legs on the ground is given as 70:
\[ 5h = 70 \] 5. Solve for \( h \): \[ h = \frac{70}{5} = 14 \] Final Answer: The number of horses is \boxed{14}.