If each number in the following sum were increased by t, the new would be 4.22. What is the value of t?

Options

A. `0.24`
B. `0.29`
C. `0.33`
D. `0.37`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
We need to find the value of \( t \) such that when each number in the sum is increased by \( t \), the new total becomes 4.22.

### Step 2: Identify the Original Sum
The original numbers given in the problem are:
- 0.65
- 0.85
- 0.38
- 0.86

### Step 3: Calculate the Original Sum
First, we need to calculate the sum of the original numbers:
\[ 0.65 + 0.85 + 0.38 + 0.86 \]
Calculating this step-by-step:
- \( 0.65 + 0.85 = 1.50 \)
- \( 1.50 + 0.38 = 1.88 \)
- \( 1.88 + 0.86 = 2.74 \)

So, the original sum is \( 2.74 \).

### Step 4: Set Up the Equation
When each number is increased by \( t \), the new sum becomes:
\[ (0.65 + t) + (0.85 + t) + (0.38 + t) + (0.86 + t) = 2.74 + 4t \]
According to the problem, this new sum equals 4.22:
\[ 2.74 + 4t = 4.22 \]

### Step 5: Solve for \( t \)
Now, we can solve for \( t \):
1. Subtract 2.74 from both sides:
\[ 4t = 4.22 - 2.74 \]
2. Calculate the right side:
\[ 4t = 1.48 \]
3. Divide both sides by 4 to isolate \( t \):
\[ t = \frac{1.48}{4} = 0.37 \]

### Conclusion
The value of \( t \) is \( 0.37 \).