Math Inequality: Points Needed To Pass
Hey everyone! Let's break down this math problem together. John needs to score at least 289 points to pass his math class, and he's already got 72, 78, and 70 points from previous tests. The big question is: which inequality will help us figure out how many more points he needs? Let's dive in and make sure John aces this class!
Understanding the Problem
So, John's goal is clear: he needs a minimum of 289 points to pass. Think of it like a target score he absolutely has to hit. Now, he's already banked some points – 72, 78, and 70 to be exact. To figure out how many more points he needs, we have to add up his current scores and see how far away he is from that 289 mark. This is where the magic of inequalities comes in. Inequalities are like equations, but instead of showing things that are exactly equal, they show relationships where things might be greater than, less than, or equal to something else. In John's case, we need an inequality that shows how his total score (including the points he still needs) relates to that 289 target.
The main idea here is to translate the word problem into a mathematical expression. The phrase "at least" is super important because it tells us we’re dealing with an inequality, not just a regular equation. When we say "at least 289," we mean 289 or more. This means we'll be using either the greater than or equal to symbol (≥) or the less than or equal to symbol (≤), but which one? To figure that out, we need to think about the relationship between John's current score, the additional points he needs, and his target score. We're looking for an inequality that shows that the sum of his existing points and the extra points he earns must be greater than or equal to 289. This ensures he meets the minimum requirement to pass the class.
Remember, we're not just crunching numbers; we're helping John succeed in his math class! By understanding the situation and breaking down the problem step by step, we can choose the correct inequality and set John on the path to passing with flying colors. We've identified the key components: John's current score, the points he needs, and the minimum passing score. Now, let's see how these pieces fit together in the form of an inequality.
Analyzing the Options
Okay, let's look at the two options we have: A) and B) . We need to figure out which one correctly represents John's situation. Option A says that the sum of his current scores (72, 78, and 70) plus any additional points he gets (represented by x) must be greater than or equal to 289. On the other hand, Option B suggests that the same sum must be less than or equal to 289.
Think about it this way: John needs to get at least 289 points to pass. Does it make sense that his total score should be less than 289? Nope! That wouldn't cut it. He needs to reach 289 or go above it. That phrase
