Question

test scores: a student needs a total of 400 points on five tests to pass a course. the student scored 82, 91, 75, 88, and 70. did the student pass the course?

Explanation:

Step1: Sum the given scores

First, we add up the scores the student has already: \( 82 + 91 + 75 + 88 + 70 \). Let's calculate that: \( 82 + 91 = 173 \), \( 173 + 75 = 248 \), \( 248 + 88 = 336 \), \( 336 + 70 = 406 \). Wait, no, wait—wait, the total needed is 480? Wait, maybe I misread. Wait, the problem says "A student needs a total of 480 points to pass a course. The student scored 82, 91, 75, 88, 70. On the final exam, what..." Wait, maybe the number of tests? Wait, maybe the initial scores are five tests? Wait, let's re-express. Let the final exam score be \( x \). The sum of the current scores plus \( x \) should be at least 480? Wait, no, maybe "pass" means reach 480. Wait, current scores: 82, 91, 75, 88, 70. Let's sum them: \( 82 + 91 = 173 \), \( 173 + 75 = 248 \), \( 248 + 88 = 336 \), \( 336 + 70 = 406 \). Then, the total needed is 480, so \( 406 + x \geq 480 \)? Wait, no, maybe the total points for the course is 480, and the student has five scores, and needs to find the final exam score? Wait, maybe the problem is: A student needs a total of 480 points to pass a course. The student scored 82, 91, 75, 88, and 70 on five tests? Wait, no, maybe the final exam is the sixth? Wait, maybe the original problem is: A student needs a total of 480 points to pass a course. The student scored 82, 91, 75, 88, 70 on five tests. What score does the student need on the final exam (sixth test) to pass? Wait, but 82+91+75+88+70 = 406. Then 480 - 406 = 74. Wait, but maybe I misread the total. Wait, maybe the total is 480, and the number of tests is six? Wait, no, the user's image is blurry, but let's assume the problem is: A student needs 480 points to pass. They have scores 82, 91, 75, 88, 70, and need to find the final exam score (let's say one more test) to reach 480. So sum of current scores: 82 + 91 + 75 + 88 + 70 = 406. Let \( x \) be the final exam score. Then \( 406 + x \geq 480 \)? Wait, no, "pass" means total is at least 480? Or is it that the total points available is 480, and the student has five scores, and the final is the sixth? Wait, maybe the problem is: A student needs a total of 480 points to pass. The student has scored 82, 91, 75, 88, 70 on five assignments. What score does the student need on the final exam (the sixth assignment) to pass? Then, total points needed: 480. Sum of current: 82+91=173, +75=248, +88=336, +70=406. So 480 - 406 = 74. So the student needs at least 74 on the final exam. Wait, but maybe the problem is different. Wait, maybe the total points for the course is 480, and the student has five tests, and the final is the sixth, so total six tests. So sum of five tests: 406, so final exam score \( x \) must satisfy \( 406 + x \geq 480 \), so \( x \geq 74 \). So the minimum score needed is 74.

Step2: Calculate the required score

Let \( S \) be the sum of the current scores: \( S = 82 + 91 + 75 + 88 + 70 = 406 \). Let \( x \) be the final exam score. The total needed is 480, so \( S + x \geq 480 \). Solving for \( x \): \( x \geq 480 - 406 = 74 \). So the student needs at least 74 on the final exam.

Answer:

The student needs at least 74 points on the final exam. (If the question was "what score does the student need on the final exam to pass", the answer is 74.)