10 horses and 15 cows eat grass of 5 acres in a certain time. How many acres will feed 15 horses and 10 cows for the same time, supposing a horse eats as much as 2 cows ?

Options

A. 40/7 acres
B. 39/8 acres
C. 40/11 acres
D. 25/9 acres

Answer

To solve the problem step by step, we will first convert the number of horses and cows into a common unit based on the information given, and then we will set up a proportion to find the required number of acres.

### Step 1: Convert horses to cows
Given that 1 horse eats as much as 2 cows, we can convert the number of horses into an equivalent number of cows.

- **10 horses = 10 * 2 = 20 cows**
- Therefore, **10 horses and 15 cows = 20 cows + 15 cows = 35 cows.**

### Step 2: Determine the total grass consumption
We know that 35 cows can eat the grass of 5 acres in a certain time.

### Step 3: Convert the second group of animals to cows
Now, we need to convert the second group of animals (15 horses and 10 cows) into cows as well.

- **15 horses = 15 * 2 = 30 cows**
- Therefore, **15 horses and 10 cows = 30 cows + 10 cows = 40 cows.**

### Step 4: Set up the proportion
We can set up a proportion based on the total number of cows and the amount of grass they consume:

\[ \frac{35 \text{ cows}}{5 \text{ acres}} = \frac{40 \text{ cows}}{x \text{ acres}} \]

### Step 5: Cross-multiply to solve for x
Cross-multiplying gives us:

\[ 35 \cdot x = 40 \cdot 5 \]

### Step 6: Simplify and solve for x
Now we can simplify and solve for x:

\[ 35x = 200 \\ x = \frac{200}{35} \\ x = \frac{40}{7} \]

### Conclusion
Thus, the number of acres that will feed 15 horses and 10 cows for the same time is \(\frac{40}{7}\) acres or approximately 5.71 acres.

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