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) [tex]$72+78+70+x\ \textless \ 289$[/tex]
B) [tex]$72+78+70+x\ \textgreater \ 289$[/tex]
C) [tex]$72+78+70+x \leq 289$[/tex]
D) [tex]$72+78+70+x \geq 289$[/tex]
Answer (2)
Calculate the sum of John's current scores: 72 + 78 + 70 = 220 .
Set up the inequality: 220 + x ≥ 289 .
Rewrite the inequality: 72 + 78 + 70 + x ≥ 289 .
The correct inequality is 72 + 78 + 70 + x ≥ 289 .
Explanation
Understanding the Problem John needs at least 289 points to pass his math class. He currently has scores of 72, 78, and 70. We need to determine which inequality represents the number of additional points, denoted as 'x', that John needs to pass the class.
Calculating Current Total Score First, calculate the sum of John's current scores: 72 + 78 + 70 = 220 .
Setting up the Inequality Now, we need to set up an inequality. John needs at least 289 points, which means his total score (current scores plus additional points) must be greater than or equal to 289. This can be written as: 220 + x ≥ 289 , which is equivalent to 72 + 78 + 70 + x ≥ 289 .
Identifying the Correct Inequality Therefore, the correct inequality is 72 + 78 + 70 + x ≥ 289 , which corresponds to option D.
Examples
Imagine you're saving up for a new bicycle that costs $289. You've already saved $72 from your birthday, $78 from doing chores, and $70 from a part-time job. The inequality 72 + 78 + 70 + x ≥ 289 helps you figure out how much more money (x) you need to save to buy the bicycle. Understanding inequalities helps you plan your savings and reach your financial goals.
John needs to achieve a total of at least 289 points to pass his math class. By calculating his current scores, which total 220, we set up the inequality 72 + 78 + 70 + x ≥ 289 , indicating how many more points he needs. Thus, the correct answer is option D.
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