Question

Mele earned scores of 75,70,92,95, and 97 points (a total of 429 points) on the first 5 tests in Economics II. Solving which of the following equations for \(s\) gives the score he needs to earn on the 6 th test to average exactly 85 points for all 6 tests? F. \(\frac{429}{5}+s=85\) G. \(\frac{429}{6}+s=85\) H. \(\frac{s+429}{5}=85\) J. \(\frac{s+429}{6}=85\) K. \(\frac{s+429}{6}=\frac{85}{100}\)

Short answer

Answer: (J) \(\frac{s+429}{6}=85\)

Step-by-step solution

Write the formula for average

The formula for calculating the average of \(n\) numbers is \(Average=\frac{Total \ space points}{Total \ space tests}\).

Plug in the given information into the formula

We know that Mele earned a total of 429 points on the first 5 tests, and we need to find the score he needs to earn on the 6th test to have an average of 85 points for all 6 tests. So the equation should be \(\frac{Total \ space points \ space on \ space first \ space 5 \ space tests \ space + \ space Score \ space on \ space 6th \ space test}{Total \ space tests}=85\), which can be written as \(\frac{429+s}{6}=85\).

Identify the equation that matches the formula

Comparing the equation \(\frac{429+s}{6}=85\) with the given options, we can see that this equation is the same as option J. \(\frac{s+429}{6}=85\) So, the correct answer is (J).

Key concepts

Average Score Calculation

Understanding how to calculate an average score is essential for success on standardized tests like the ACT. An average is a measure of central tendency that indicates the typical value of a set of numbers. To calculate the average score, you sum up all the individual scores and then divide the sum by the total number of scores.Let's consider Mele's scenario from our exercise. He scored 75, 70, 92, 95, and 97 points on the first 5 tests. To find the average score he aims for over all six tests, we apply this formula:

\[ Average = \frac{\text{Total points}}{\text{Total tests}} \]To ensure he averages exactly 85 points across six tests, we calculate the needed score for the 6th test. We establish the following equation based on the formula: \[ \frac{\text{Total points from first 5 tests} + \text{Score on 6th test}}{6} = 85 \]Substituting Mele's points, we get:\[ \frac{429 + s}{6} = 85 \]By solving for \(s\), Mele can find out the exact score needed on his 6th test to achieve his average score goal.

Algebra in Standardized Tests

Algebraic concepts are frequently tested in standardized tests like the ACT. A solid foundation in algebra can help students solve a variety of problems, including those related to average score calculations. In the given problem, an equation must be set up and solved for a variable, which is a common type of algebraic problem.

Identifying the Correct Equation

When presented with multiple choices, as in our exercise, it's essential to understand the structure of the equations and what they represent. Here are a few tips to identify the right algebraic equation:

• Sum up the known values and include the unknown variable for the score (in this case, \(s\)).
• The total points are divided by the number of tests—which includes the test for which the score is yet to be determined.
• The result should equal the desired average score.

By recognizing these algebraic patterns, students can quickly eliminate incorrect choices and focus on solving the correct equation.

ACT Test Practice Problems

Getting familiar with ACT practice problems is crucial for scoring well on the actual test. Practice problems help students apply various concepts and sharpen their problem-solving skills.

How to Approach Practice Problems

Start with a clear understanding of the problem's requirements. Then identify which mathematical operations and formulas are needed. Work systematically through each step, avoiding any rush to choose an answer—especially on multiple-choice problems where similar-looking options may lead to common mistakes.

When faced with a practice problem similar to Mele's average score calculation, try the following approach:

• Read the problem carefully and note all the given information.
• Write down the related formula or concept you need to apply—like the average score formula.
• Plug the given information into the formula and solve the equation systematically for the required variable.
• Review each option provided and eliminate those that don't fit logically based on your equation.

Remember, consistent practice is the key to gaining confidence and improving speed and accuracy on the ACT.