Question

A company earned a profit of \(\$ 8.0\) million each year for 3 consecutive years. For each of the next 2 years the company earned a profit of \(\$ 9.0\) million. For this "s-year period, what was the company's average yearly profit, in millions of dollars? F. 8.25 G. 8.25 H. 8.4 J. 8.5 K. 8.6

Short answer

Answer: H. \$8.4 million

Step-by-step solution

Compute the total profit for the first 3 years

First, we need to calculate the total profit for the first 3 years. The company earned a profit of \(\$8.0\) million each year for 3 consecutive years. We will multiply the yearly profit by the number of years: \(3 * \$ 8.0\) million = \(\$ 24.0\) million.

Compute the total profit for the next 2 years

Next, we need to calculate the total profit for the following 2 years. In these two years, the company earned a profit of \(\$9.0\) million each year. We will multiply the yearly profit by the number of years: \(2 * \$ 9.0\) million = \(\$ 18.0\) million.

Compute the overall total profit for the 5-year period

Now that we have the total profit for the first 3 years and the next 2 years, we can add them up to get the total profit for the whole 5-year period: \(\$ 24.0\) million + \(\$ 18.0\) million = \(\$ 42.0\) million.

Calculate the average yearly profit

To calculate the average yearly profit, we will divide the overall total profit by the total number of years (5 years): \(\dfrac{\$ 42.0 \text{ million}}{5} = \$ 8.4\) million.

Choose the correct answer from the given choices

We find that the average yearly profit for the 5-year period is \(\$ 8.4\) million, so the correct answer is H. 8.4.

Key concepts

Profit Calculation

Understanding how to calculate profit is essential for any student studying business or preparing for exams like the ACT. In its simplest form, profit calculation involves subtracting expenses from revenue to determine earnings. However, in many academic and real-world scenarios, including the one from our original exercise, the focus is on determining total and average profits over a period of time.

To calculate total profit over several years, as in the exercise, you need to multiply the annual profit by the number of years for each different profit amount and then sum these totals. This gives you the aggregate profit for the timeframe in question. Students should ensure that they apply the correct profit figure to the right number of years to avoid miscalculations. It's a primary skill that has practical applications in budgeting, finance, and economics.

Arithmetic Mean

The arithmetic mean, commonly known as the average, is a measure that is frequently used in various fields, including statistics, finance, and mathematics. It represents the central value of a discrete set of numbers. Calculating the arithmetic mean involves adding up all the values and then dividing by the number of values.

In the context of our exercise, the arithmetic mean is used to find the average yearly profit over a given period. The process can be summarized in two steps: First, find the total profit for the period, and second, divide that total by the number of years. It is crucial to include all years in the calculation to get an accurate average. When presenting arithmetic mean calculations, clarity in each step is imperative for students to understand and replicate the process on their own.

ACT Math Problems

The ACT Math section tests students on a range of mathematical concepts, which includes problems related to profit calculation and arithmetic means. Understanding these concepts is not only pivotal for achieving a good score on the ACT but also for their practical applications outside standardized testing.

Profit calculation problems within the ACT might involve linear equations, percentages, and understanding of basic arithmetic operations, which are all integral to business mathematics. These math problems require clear logical reasoning and step-by-step calculation to solve. As with any standardized test, practice, familiarity with the format of the questions, and a methodical approach to solving problems are the keys to success. It's helpful for students to learn how to break down problems into smaller, manageable parts, just like the exercise demonstrated, to improve accuracy and efficiency on the test.