To solve this problem, we can use the formula for the average of three test scores:

$\text{Average} = \frac{\text{Score 1} + \text{Score 2} + \text{Score 3}}{3}$

Jim wants an average of at least 75, and we know his scores on the first two tests are 68 and 86.

Let $x$ represent the score Jim needs on his third test. The equation becomes:

$\frac{68 + 86 + x}{3} \geq 75$

Now, solve for $x$.

1. First, simplify the numerator:

$\frac{154 + x}{3} \geq 75$

2. Multiply both sides by 3 to eliminate the denominator:

$154 + x \geq 225$

3. Subtract 154 from both sides:

$x \geq 225 - 154$

$x \geq 71$

Therefore, Jim must score at least 71 on his third test to maintain an average of 75 or greater.

The correct answer is B. At least 71.

Would you like a more detailed explanation or help with related questions?

Here are 5 related questions:

1. How is the formula for averages derived?
2. What would happen if Jim wants an average of 80?
3. How does weighting affect test scores in averages?
4. Can averages include decimals, and how would that change the result?
5. What strategies can be used to ensure a desired average?

Tip: When calculating averages, make sure to account for all values equally unless specified otherwise.