Problem 137 - Prealgebra

Question

Test scores A students 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?

Step-by-Step Solution

Answer

Yes, the student passed. They scored 406 points and only needed 400.

Step 1 - Add up the scores

Sum the test scores to find the total number of points the student earned. Add the scores: 82, 91, 75, 88, and 70. The equation is: 82 + 91 + 75 + 88 + 70

Step 2 - Calculate the total points

Perform the addition from Step 1 to find the total points. 82 + 91 = 173 173 + 75 = 248 248 + 88 = 336 336 + 70 = 406

Step 3 - Compare the total to the passing score

The student needs at least 400 points to pass. Compare the total points calculated (406) to the required amount (400).

Step 4 - Determine if the student passed

The student earned 406 points, which is more than the required 400 points. Therefore, the student passed the course.

Key Concepts

Addition

To find out if the student passed the course, the first step is to add up all the test scores. Addition is a fundamental mathematical operation that combines numbers to get a total. Here, we start by adding the scores one by one: 82, 91, 75, 88, and 70. When you sum these numbers, you're performing a series of additions.

Let's break it down further:
1. Add 82 and 91 to get 173.
2. Add 173 and 75 to get 248.
3. Add 248 and 88 to get 336.
4. Finally, add 336 and 70 to get 406.

By adding these scores step by step, you ensure accuracy and make it easier to track your progress.

Comparison

After you have the total points from adding the test scores, the next step is to compare this total to the passing score. Comparison in mathematics is used to determine if one number is greater than, less than, or equal to another number. Here, we need to compare the student's total score, which is 406, to the required passing score of 400.

If the total score (406) is greater than or equal to the passing score (400), then the student passes the course. In this case, 406 is greater than 400, meaning the student has successfully passed.

Passing Score

A passing score is the number of points a student must earn to pass a test or course. In this exercise, the passing score is set at 400 points. This is the benchmark or criterion that the student needs to meet or exceed to be considered successful in the course. Schools and educational institutions often set a specific passing score to maintain academic standards and ensure consistency across evaluations.

Knowing the passing score is crucial because it gives students a clear goal to aim for. It helps them gauge their performance and understand what is required to succeed.

Points Total

The points total is the sum of all points a student earns across different assessments or tests. In this example, the total points are calculated by adding the individual test scores: 82, 91, 75, 88, and 70. The points total is an important measure of overall performance, showing how well a student has done over the course of multiple evaluations.

For this student, the points total is 406, which is derived from summing all the individual test scores. Having a points total higher than the passing score of 400 indicates that the student has performed sufficiently well to pass the course. Each test contributes to this total, highlighting the importance of consistent effort across all tests.