Jaime is preparing for a bicycle race. His goal is to bicycle an average of at least 280 miles per week for 4 weeks. He bicycled 240 miles the first week, 310 miles the second week, and 320 miles the third week. Which inequality can be used to represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal?

Options

A. `(240+310+320)/3+ x ge 280`
B. `240+310+320 ge x (280)`
C. `240/4+310/4+320/4+ x ge 280`
D. `240+310+320 +x ge 4 (280)`

Explanation

To solve the problem, we need to determine an inequality that represents the number of miles Jaime could bicycle in the fourth week to achieve his goal of an average of at least 280 miles per week over four weeks.

### Step-by-Step Solution:

1. **Understand the Average Formula**:
The average of a set of numbers is calculated by dividing the sum of the numbers by the count of the numbers. In this case, we want the average of the miles bicycled over four weeks.

2. **Set Up the Average Equation**:
Let \( x \) be the number of miles Jaime bicycles in the fourth week. The total miles bicycled over the four weeks will be:
\[ 240 + 310 + 320 + x \]
The average for the four weeks can be expressed as:
\[ \text{Average} = \frac{240 + 310 + 320 + x}{4} \]

3. **Set Up the Inequality**:
Jaime wants the average to be at least 280 miles. Therefore, we can set up the inequality:
\[ \frac{240 + 310 + 320 + x}{4} \geq 280 \]

4. **Multiply Both Sides by 4**:
To eliminate the fraction, multiply both sides of the inequality by 4:
\[ 240 + 310 + 320 + x \geq 4 \times 280 \]

5. **Calculate the Right Side**:
Calculate \( 4 \times 280 \):
\[ 4 \times 280 = 1120 \]
So, the inequality now looks like:
\[ 240 + 310 + 320 + x \geq 1120 \]

6. **Combine the Known Values**:
Now, add the miles from the first three weeks:
\[ 240 + 310 + 320 = 870 \]
Thus, the inequality simplifies to:
\[ 870 + x \geq 1120 \]

7. **Isolate \( x \)**:
To find \( x \), subtract 870 from both sides:
\[ x \geq 1120 - 870 \]
Calculate \( 1120 - 870 \):
\[ 1120 - 870 = 250 \]
Therefore, we have:
\[ x \geq 250 \]

### Final Inequality:
The inequality that represents the number of miles Jaime could bicycle in the fourth week to meet his goal is:
\[ x \geq 250 \]