Set 10: Linear Inequalities (Advanced)

Choice A is correct. Choice A is the correct answer. The average formula is $\frac{\text{Sum of terms}}{\text{Number of terms}}$. 1. Set up: $\frac{78 + 85 + 92 + x}{4} \geq 88$ 2. Sum knowns: $255+ x$ 3. Multiply by 4: $255+ x \geq 88 \times 4 = 352$ 4. Subtract 255: $x \geq 352 - 255$ 5. Result: $x \geq 97$ Strategic Tip: For average problems, multiply the target average by the total number of items to find the required sum. Choice B is incorrect because scoring the average (88) would bring the total average down since the current average is $\frac{255}{3} = 85$. Choice C is incorrect because it sets a maximum limit instead of a minimum requirement. Choice D is incorrect because 352 is the required total sum, not the single test score.