Decoding the Pattern in the Equations

The problem presents two equations with unknown operations represented by 'D', 'E', and 'F'. We need to find the pattern to solve the third expression.

• Equation 1: 37 D 18 E 84 F 21 = 51
• Equation 2: 57 D 28 E 90 F 15 = 79

Let's test arithmetic operations. We observe that if 'D' represents addition (+), 'E' represents subtraction (-), and 'F' represents division (/), the equations hold true, following the standard order of operations (Division first, then Addition/Subtraction).

Verifying the Pattern

For Equation 1:

We apply the proposed operations: $37 + 18 - 84 \div 21$

1. Division: $84 \div 21 = 4$
2. Addition: $37 + 18 = 55$
3. Subtraction: $55 - 4 = 51$

This matches the given result.

For Equation 2:

We apply the same operations: $57 + 28 - 90 \div 15$

1. Division: $90 \div 15 = 6$
2. Addition: $57 + 28 = 85$
3. Subtraction: $85 - 6 = 79$

This also matches the given result. The pattern is confirmed.

Solving the Target Expression

Now, we apply the identified pattern (Number1 + Number2 - Number3 / Number4) to the target expression: 14 D 17 E 8 F 4.

Expression: $14 + 17 - 8 \div 4$

1. Division: Calculate $8 \div 4 = 2$.
2. Addition: Calculate $14 + 17 = 31$.
3. Subtraction: Calculate $31 - 2 = 29$.

Therefore, the value of the expression is 29.