Question

Three investors, \(A, B,\) and \(C,\) divide the profits from a business enterprise in the ratio of \(5: 7: 8,\) respectively. If investor A earned \(\$ 3,500,\) how much money did investors \(\mathrm{B}\) and \(\mathrm{C}\) earn in total? $$\begin{array}{c} \$ 4,000 \\ \$ 4,900 \\ \$ 5,600 \\ \$ 9,500 \\ \$ 10,500 \end{array}$$

Short answer

\$ 10,500

Step-by-step solution

Understand the Ratio

The given profit-sharing ratio among Investors A, B, and C is \(5:7:8\). This means for every 5 parts that A gets, B gets 7 parts, and C gets 8 parts.

Total Parts in the Ratio

Calculate the total number of parts in the ratio. We add the parts of A, B, and C together: 5 (A) + 7 (B) + 8 (C) = 20 parts.

Calculate the Value of One Part

Investor A's earnings are given as \(\$ 3,500\). We know that A's share is 5 parts of the total profit. Thus, the value of one part is calculated as: \[ \text{Value of one part} = \frac{\$ 3,500}{5} = \$ 700. \]

Calculate Investor B's Earnings

Using the value of one part, calculate B's earnings: \( \text{B's earnings} = 7 \text{ parts} \times \$ 700 = \$ 4,900. \)

Calculate Investor C's Earnings

Similarly, calculate C's earnings: \( \text{C's earnings} = 8 \text{ parts} \times \$ 700 = \$ 5,600. \)

Add B and C's Earnings

Finally, add the earnings of investors B and C to get the total amount earned by them together: \( \$ 4,900 + \$ 5,600 = \$ 10,500. \)

Key concepts

Profit Sharing

Profit sharing is the process of dividing the profits of a business venture among its investors or partners. In our example, three investors share the profits. The ratio system is used to share profits according to their contributions. This concept ensures fairness and proportional distribution of earnings among participants.
Profits are divided based on predetermined ratios agreed upon by the partners. These ratios reflect each partner's contribution to the business, whether monetary or otherwise.

Ratio Calculations

Ratio calculations are essential in determining how quantities are shared among participants proportionally. Here, the given ratio is 5:7:8 for investors A, B, and C.
To find the total number of parts in a ratio:

• Add the parts together: 5 + 7 + 8 = 20 parts.
• Divide the known monetary value by the number of parts corresponding to that value to find the worth of one part.

This method allows us to break down and understand each investor's share based on the given ratio and total profit.

Step-by-Step Math Solutions

Breaking down a problem into step-by-step solutions helps simplify and understand complex calculations.
Our step-by-step breakdown includes:
1. Understanding the ratio.
2. Calculating the total parts of the ratio.
3. Finding the value of one part.
4. Using this to find the profit for each investor.
5. Summing relevant parts to find combined figures.
These clear and logical steps ensure that even intricate problems are resolved with ease, promoting better comprehension and problem-solving skills.

Investment Returns

Investment returns are the gains or losses earned from investing in a business or project. In this case, investors A, B, and C receive returns from their business venture.
Their returns are calculated based on the given ratio and the total profit.

• Investor A's earnings: 5 parts, which equals $3,500.
• Investor B's earnings: 7 parts, calculated from the value per part.
• Investor C's earnings: 8 parts, also calculated similarly.

Understanding investment returns and how they are calculated can help investors make informed decisions and better assess the profitability of their investments.

Business Enterprise

A business enterprise is an organization involved in commercial, industrial, or professional activities. In this context, it refers to a venture shared by three investors.
Key aspects include:

• Collaborative effort and financial contributions.
• Profit-sharing mechanisms, which ensure fair distribution.
• Understanding and calculating ratios for equitable profit division.

Analyzing profit distribution within a business enterprise helps in understanding the financial structure and return on investments for all involved partners.