Final Answer:
7 times the pin's position minus 31 equals 4, leading to the equation 7p - 31 = 4, where 'p' represents the pin's position.Thus the correct equation is option (a) 7p - 31 = 4.
Step-by-step explanation:
To translate the given sentence into an equation, we need to focus on the phrase "31 less than 7 times the position of the pin is 4." This can be mathematically expressed as "7 times the position of the pin, decreased by 31, equals 4." In mathematical terms, "7 times the position of the pin" translates to 7p, where 'p' represents the position of the pin. "31 less than" indicates subtraction, so it becomes "-31." The phrase "is" indicates equality, leading to the equation "7p - 31 = 4." Solving this equation by isolating 'p' yields the value of the pin's position.
To break down the steps further, the phrase "7 times the position of the pin" is represented as 7p, indicating that the position is multiplied by 7. "31 less than" implies subtracting 31 from this product. Finally, the result is equal to 4. By rearranging terms and solving for 'p,' we find the position of the pin.
Therefore, the correct equation to represent the statement "31 less than 7 times the position of the pin is 4" is indeed 7p - 31 = 4. This equation accurately portrays the relationship between the pin's position and the given value of 4 after 31 is subtracted from 7 times the position of the pin.