The maximum value of F in the following equation 5E9 + 2F8 + 3G7 = 1114 is where E, F, G each stands for any digit.

Options

A. 8
B. 9
C. 7
D. 5

Answer

To solve the equation \(5E9 + 2F8 + 3G7 = 1114\) and find the maximum value of \(F\), we can follow these steps:

### Step 1: Understand the equation
The equation consists of three terms: \(5E9\), \(2F8\), and \(3G7\). Each letter (E, F, G) represents a single digit (0-9).

### Step 2: Break down the equation
We can express the equation in terms of digits:
- \(5E9\) can be expressed as \(500 + 10E + 9\)
- \(2F8\) can be expressed as \(200 + 10F + 8\)
- \(3G7\) can be expressed as \(300 + 10G + 7\)

So, the equation becomes:
\[ (500 + 10E + 9) + (200 + 10F + 8) + (300 + 10G + 7) = 1114 \]

### Step 3: Combine like terms
Combining all the constants and variables:
\[ 500 + 200 + 300 + 10E + 10F + 10G + 9 + 8 + 7 = 1114 \]
This simplifies to:
\[ 1006 + 10E + 10F + 10G = 1114 \]

### Step 4: Isolate the variable terms
Subtract 1006 from both sides:
\[ 10E + 10F + 10G = 1114 - 1006 \]
This simplifies to:
\[ 10E + 10F + 10G = 108 \]

### Step 5: Simplify further
Dividing the entire equation by 10 gives:
\[ E + F + G = 10.8 \]
Since \(E\), \(F\), and \(G\) are digits, we can round down to \(E + F + G = 10\).

### Step 6: Maximize \(F\)
To maximize \(F\), we can minimize \(E\) and \(G\). The smallest values for \(E\) and \(G\) are both 0. Therefore:
\[ 0 + F + 0 = 10 \implies F = 10 \]
However, since \(F\) must be a single digit (0-9), we cannot have \(F = 10\). Therefore, we set \(E = 0\) and \(G = 1\):
\[ 0 + F + 1 = 10 \implies F = 9 \]

### Step 7: Conclusion
Thus, the maximum value of \(F\) is 9.