John must have at least 289 test points to pass his math class. He already has test scores of 72, 78, and 70. Which inequality will tell him at least how many more points he needs to pass the class? A. 72 + 78 + 70 + x ≤ 289 B. 72 + 78 + 70 + x > 289 C. 72 + 78 + 70 + x < 289 D. 72 + 78 + 70 + x ≥ 289
The Correct Answer and Explanation is:
Correct Answer: D. 72 + 78 + 70 + x ≥ 289
Explanation
To determine how many more points John needs to pass his math class, we first need to understand the requirement and what he has already earned.
John must have at least 289 test points to pass. The phrase “at least” means that 289 is the minimum he needs, and he can earn more than or equal to that amount and still pass. In math, “at least” is represented by the greater than or equal to (≥) symbol.
John’s current scores are:
- First test: 72
- Second test: 78
- Third test: 70
Adding up his current test scores:72+78+70=22072 + 78 + 70 = 22072+78+70=220
Let xxx represent the number of points John needs on his next test. To find out how many more points he needs to reach or exceed 289 points, we add xxx to his current total of 220 and write the inequality:220+x≥289220 + x \geq 289220+x≥289
This inequality means the sum of his current scores and the next test score must be greater than or equal to 289.
We can simplify the inequality:220+x≥289220 + x \geq 289220+x≥289
Subtract 220 from both sides:x≥69x \geq 69x≥69
So, John needs at least 69 more points on the next test to pass.
Now looking at the original multiple-choice options:
- A uses “≤” (less than or equal to), which doesn’t match “at least”
- B uses “>” (greater than), which excludes exactly 289
- C uses “<” (less than), which is incorrect
- D uses “≥” (greater than or equal to), which correctly represents “at least”
Therefore, the correct inequality is:72+78+70+x≥28972 + 78 + 70 + x \geq 28972+78+70+x≥289
✔️ Answer: D
