Question
2. FARMING The ratio of goats to sheep at a university research farm is \( 4: 7 \). The number of sheep at the farm is 28 . What is the number of goats?
Ask by Coleman Frank. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
There are 16 goats at the farm.
Solution
To determine the number of goats based on the given ratio, follow these steps:
### Given:
- **Ratio of goats to sheep**: \( \frac{4}{7} \)
- **Number of sheep**: 28
### Step-by-Step Solution:
1. **Understand the Ratio**:
The ratio \( \frac{4}{7} \) means that for every 4 goats, there are 7 sheep.
2. **Set Up the Proportion**:
Let \( G \) represent the number of goats. According to the ratio:
\[
\frac{G}{28} = \frac{4}{7}
\]
3. **Solve for \( G \)**:
To find the value of \( G \), cross-multiply:
\[
7G = 4 \times 28
\]
\[
7G = 112
\]
\[
G = \frac{112}{7}
\]
\[
G = 16
\]
### Answer:
There are **16 goats** at the farm.
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Simplify this solution Extra Insights
At the university research farm, if the ratio of goats to sheep is \( 4: 7 \), we know that for every 4 goats, there are 7 sheep. Given that there are 28 sheep, we can set up a proportion to find the number of goats. Since \( 7 \) represents the sheep in the ratio and there are \( 28 \) sheep at the farm, we can calculate how many groups of \( 7 \) fit into \( 28 \): \( 28 \div 7 = 4 \). This means there are \( 4 \) groups of sheep. Since each group has \( 4 \) goats, we simply multiply: \( 4 \times 4 = 16 \). Therefore, there are 16 goats at the farm. The number of goats at the farm is 16.
