7
algebra

A student has test scores of 78, 85, and 92. What must they score on the fourth test (xx) to have an average of at least 88?

A

x97x \geq 97

B

x88x \geq 88

C

x97x \leq 97

D

x352x \geq 352

Correct Answer: A

Choice A is the correct answer. The average formula is Sum of termsNumber of terms\frac{\text{Sum of terms}}{\text{Number of terms}}.

  1. Set up: 78+85+92+x488\frac{78 + 85 + 92 + x}{4} \geq 88
  2. Sum knowns: 255+x255 + x
  3. Multiply by 4: 255+x88×4=352255 + x \geq 88 \times 4 = 352
  4. Subtract 255: x352255x \geq 352 - 255
  5. Result: x97x \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 2553=85\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.