Question

By applying which of the following meanings of letters will the expression \(8 \, R \, 8 \, P \, 8 \, S \, 8 \, Q \, 8 = 57\) be true? \flushleft

• A. \( P \) means \( \times \), \( Q \) means \( - \), \( R \) means \( \div \), \( S \) means \( + \)
• B. \( P \) means \( \div \), \( Q \) means \( \times \), \( R \) means \( \div \), \( S \) means \( - \)
• C. \( P \) means \( + \), \( Q \) means \( - \), \( R \) means \( \times \), \( S \) means \( \div \)
• D. \( P \) means \( - \), \( Q \) means \( \times \), \( R \) means \( \div \), \( S \) means \( + \)

Hint:

When solving equations with unknown operations, systematically substitute each possible operation and evaluate to find the correct solution.

Answer 1

The Correct Option is C

Step-by-step evaluation of each option:
Option 1:
\[ 8 \div 8 \times 8 + 8 - 8 = 1 \times 8 + 8 - 8 = 8 + 8 - 8 = 8 \] Result is \( 8 \), not \( 57 \).
Option 2:
\[ 8 \div 8 \div 8 - 8 \times 8 = 1 \div 8 - 64 = 0.125 - 64 = -63.875 \] Result is \( -63.875 \), not \( 57 \).
Option 3:
\[ 8 \times 8 + 8 \div 8 - 8 = 64 + 1 - 8 = 57 \] Result is \( 57 \), which is correct.
Option 4:
\[ 8 \div 8 - 8 + 8 \times 8 = 1 - 8 + 64 = 57 \] Result is also \( 57 \), which is correct.