The sum of n and the product 3 × n is 12. What is the value of n?

Rationale

The value of n is 3.

To solve the equation \( n + 3n = 12 \), we simplify it to \( 4n = 12 \) and then divide both sides by 4, yielding \( n = 3 \).

A (2) YOUR ANSWER

If \( n = 2 \), then the sum \( n + 3n = 2 + 3(2) = 2 + 6 = 8 \), which does not equal 12. Therefore, this choice is incorrect.

B (3) CORRECT

Substituting \( n = 3 \) into the equation gives \( n + 3n = 3 + 3(3) = 3 + 9 = 12 \), confirming that this value satisfies the original condition.

C (4) YOUR ANSWER

For \( n = 4 \), we calculate \( n + 3n = 4 + 3(4) = 4 + 12 = 16 \), which exceeds 12. Thus, this option does not hold true.

D (4 ½) YOUR ANSWER

If \( n = 4 \frac{1}{2} \), or 4.5, substituting gives \( n + 3n = 4.5 + 3(4.5) = 4.5 + 13.5 = 18 \), which is also not equal to 12. Therefore, this choice is incorrect.

Conclusion

The sum of \( n \) and the product \( 3 \times n \) equals 12 when \( n \) is equal to 3, as confirmed by substituting this value back into the equation. The other choices result in sums that do not equal 12, which verifies that they are indeed incorrect. Understanding how to manipulate and solve equations is key to determining the correct values of variables in algebraic expressions.