Question

Kalino earned \(85,95,93,\) and 80 points on the 4 tests, each worth 100 points, given so far this term. How many points must he earn on his fith test, also worth 100 points, to average 90 points for the 5 tests given this term? A. 87 B. 88 C. 90 D. 92 E. 97

Short answer

Answer Choices: A: 87 B: 88 C: 90 D: 92 E: 97 Solution: Step 1: Calculate the total points needed for an average of 90 points over five tests. Total points needed = 90 * 5 Total points needed = 450 Step 2: Calculate the total points Kalino has scored so far. Total points so far = 85 + 95 + 93 + 80 Total points so far = 353 Step 3: Find the required points on the fifth test. Points needed on fifth test = (Total points needed) - (Total points so far) Points needed on fifth test = 450 - 353 Points needed on fifth test = 97 Step 4: Check the result against the answer choices. The correct answer is E: 97. Kalino needs to score 97 points on his fifth test to achieve an average of 90 points on all five tests.

Step-by-step solution

Calculate the total points needed for an average of 90 points over five tests

To find the total points needed for an average of 90 points over five tests, we need to multiply the average (90) by the number of tests (5): Total points needed = 90 * 5 Calculate the result.

Calculate the total points Kalino has scored so far

We need to add the points Kalino scored on the first four tests to find the total points he has scored so far: Total points so far = 85 + 95 + 93 + 80 Calculate the result.

Find the required points on the fifth test

To find how many points Kalino needs to score on his fifth test, subtract the total points he scored so far from the total points needed for an average of 90 points over five tests: Points needed on fifth test = (Total points needed) - (Total points so far) Plug in the values obtained in steps 1 and 2, and calculate the result.

Check the result against the answer choices

Compare the result obtained in step 3 with the given answer choices (A: 87, B: 88, C: 90, D: 92, E: 97) to determine the correct answer.

Key concepts

Average Calculation

Understanding how to calculate an average, or arithmetic mean, is a fundamental skill in math, affecting many aspects of one's academic journey, particularly in standardized tests like the ACT. To find an average, you sum up all the numbers and then divide the total by the number of values you've added. In the exercise where Kalino needs to average 90 points over five tests, you calculate the total points by summing his scores on the first four tests and divide the result by four to check his current average. This is critical because knowing his current average points per test helps to set a target for the fifth test.

Also, be aware of the difference between what Kalino has scored and what he aims to score – the goal to average 90 points. By determining how far he is from this goal after the first four tests, you can accurately calculate what he needs on the final test. The skill of average calculation is integral across various academic disciplines and everyday life. Keeping a steady pace of practice on such problems can significantly enhance a student's mathematical fluency.

Arithmetic Mean

Role in Academic Scenarios

Arithmetic mean, often simply called the average, is especially important when evaluating academic performance. When you calculate the arithmetic mean of test scores, like those of Kalino's, you get valuable information about his overall performance relative to a consistent standard – for instance, the 90-point goal. This measure allows educators, students, and parents to track progress over time.

Application in Problem Solving

Beyond the academic record, understanding the arithmetic mean plays a crucial role in problem-solving. Whether you're dealing with test scores, finding rates, or even interpreting data in science experiments, this concept is ubiquitous. In Kalino's case, it enables him to set measurable goals and make strategic decisions about how to approach his final test, embodying the practical utility of the arithmetic mean.

ACT Math Strategies

While the specific exercise involving Kalino's test scores may not appear in the ACT precisely as described, the underlying principles are the same. ACT Math requires a clear and efficient approach to problem-solving. For a test like the ACT, knowing shortcuts and understanding the concept of averaging can save valuable time. Here's how to apply this in a testing context:

• Process of Elimination: Once Kalino calculates the points needed on the final test, he can eliminate any answer choices that don't match. This technique also works well on the ACT, often leaving one or two probable answers.
• Time Management: Estimating the answer before solving can help you manage your time better. If Kalino's scores have been consistently high, he likely wouldn't need an unusually high score on the last test to average 90. This technique allows quick elimination of outliers.
• Backsolve: Starting with the provided options, especially on multiple-choice exams like the ACT, and working backward can be a faster path to the solution.

Implementing these strategies during test prep allows students to perform more effectively in the actual testing environment, much like how Kalino can plan his approach for achieving his desired average score on the next test.