Find `Q` in the addition.
`({:(," "31Q),(,+ 1Q3" "):}) /(" "501)`

Options

A. 8
B. 2
C. 4
D. 6

Explanation

To find the value of \( Q \) in the addition \( 31Q + 1Q3 = 501 \), we will follow these steps:

### Step 1: Set up the equation
We start with the equation:
\[ 31Q + 1Q3 = 501 \]

### Step 2: Break down the addition
We can express the numbers in terms of \( Q \):
- \( 31Q \) can be expressed as \( 310 + Q \)
- \( 1Q3 \) can be expressed as \( 100 + 10Q + 3 \)

Now, substituting these expressions into the equation gives us:
\[ (310 + Q) + (100 + 10Q + 3) = 501 \]

### Step 3: Simplify the equation
Combine like terms:
\[ 310 + 100 + 3 + Q + 10Q = 501 \]
This simplifies to:
\[ 413 + 11Q = 501 \]

### Step 4: Isolate \( Q \)
Now, we need to isolate \( Q \) by subtracting 413 from both sides:
\[ 11Q = 501 - 413 \]
Calculating the right side gives:
\[ 11Q = 88 \]

### Step 5: Solve for \( Q \)
Now, divide both sides by 11:
\[ Q = \frac{88}{11} \]
Calculating this gives:
\[ Q = 8 \]

### Step 6: Verify the solution
To ensure our solution is correct, we can substitute \( Q = 8 \) back into the original numbers:
- \( 31Q = 318 \)
- \( 1Q3 = 183 \)

Now, check the addition:
\[ 318 + 183 = 501 \]
Since this is correct, our solution is verified.

### Final Answer:
\[ Q = 8 \]

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