On 4 sales, Matt received commissions of `$300, $40, $x, and $140`. Without the `$x`, his average commission would be `$50` lower. What is x?

Answer

To solve the problem, we need to find the value of \( x \) based on the information provided about Matt's commissions. Let's break it down step by step.

### Step 1: Understand the Average Formula
The average of a set of numbers is calculated by dividing the sum of those numbers by the count of the numbers.

### Step 2: Calculate the Average Without \( x \)
Matt's commissions without \( x \) are \( 300, 40, \) and \( 140 \). We need to find the average of these three values.

1. **Sum the commissions without \( x \)**:
\[ 300 + 40 + 140 = 480 \]

2. **Count the number of commissions**:
There are 3 commissions.

3. **Calculate the average**:
\[ \text{Average without } x = \frac{480}{3} = 160 \]

### Step 3: Set Up the Equation for Average With \( x \)
With \( x \) included, the commissions are \( 300, 40, x, \) and \( 140 \).

1. **Sum the commissions with \( x \)**:
\[ 300 + 40 + x + 140 = 480 + x \]

2. **Count the number of commissions**:
There are 4 commissions.

3. **Calculate the average with \( x \)**:
\[ \text{Average with } x = \frac{480 + x}{4} \]

### Step 4: Set Up the Equation Based on the Given Condition
According to the problem, the average with \( x \) is $50 higher than the average without \( x \):
\[ \text{Average with } x = \text{Average without } x + 50 \]
Substituting the values we calculated:
\[ \frac{480 + x}{4} = 160 + 50 \]
\[ \frac{480 + x}{4} = 210 \]

### Step 5: Solve the Equation
Now, we will solve for \( x \).

1. **Multiply both sides by 4 to eliminate the fraction**:
\[ 480 + x = 840 \]

2. **Isolate \( x \)**:
\[ x = 840 - 480 \]
\[ x = 360 \]

### Conclusion
The value of \( x \) is \( 360 \).