Problem 146 - Elementary and Intermediate Algebra

Question

Bankruptcy. After filing for bankruptcy, a company was able to pay its creditors only 15 cents on the dollar. If the company owed a lumberyard 9,712 dollars, how much could the lumberyard expect to be paid?

Step-by-Step Solution

Answer

The lumberyard will be paid $1,456.80.

Step 1: Understanding the Problem

The problem states that a company owes $9,712 to a lumberyard and is able to pay back only 15 cents on the dollar after filing for bankruptcy. We need to find out how much money the lumberyard will receive.

Step 2: Identifying the Value per Dollar

The company can pay 15 cents for every dollar owed. Therefore, each dollar is equivalent to 0.15 dollars in terms of repayment.

Step 3: Calculating the Payment Amount

To find out how much the lumberyard will receive, multiply the total amount owed by the repayment percentage: \( \text{Payment} = 9,712 \times 0.15 \).

Step 4: Completing the Calculation

Carry out the multiplication to find the payment amount: \( \text{Payment} = 9,712 \times 0.15 = 1,456.8 \). Therefore, the lumberyard will receive $1,456.80.

Key Concepts

Percentage Calculations

Percentage calculations are a handy mathematical tool. They allow us to understand parts per hundred of any given value. Whether we are calculating discounts, marks on a test, or repayments, percentages make it easy to handle proportional data.

Here's how they work in the context of bankruptcy: After filing for bankruptcy, a company might be able to repay only a certain percentage of its debts. In the exercise at hand, the company can only pay 15 cents for every dollar owed. This means it is paying back 15% of its original debt.

To calculate how much the lumberyard will receive, you apply this percentage to the total amount owed. In algebraic terms, you multiply the owed amount by the repayment percentage as a decimal:

• Convert the percentage to a decimal by dividing by 100: 15% becomes 0.15.
• Multiply that decimal by the total dollar amount owed.

The calculation shows how much the lumberyard will be paid based on the terms of the bankruptcy.

Bankruptcy Math Problems

Bankruptcy math problems often involve calculating how much creditors will receive when debtors can't fully repay what they owe. In these scenarios, the debtor might offer creditors a percentage of the total debt in settlement.

For our lumberyard example, understanding that the company can only pay 15 cents per dollar clarifies what portion of the debt will be repaid. The mathematics behind this ensure that creditors and debtors can come to a fair and clear resolution.

These problems typically involve steps like:

• Identifying the amount owed and the percentage that can be paid back.
• Performing percentage calculations to determine the repayment.

Solutions like these not only provide a result but also teach financial decision-making and help creditors know what to expect during a bankruptcy process.

Financial Literacy in Algebra

Financial literacy is crucial, and algebra can help make sense of financial problems. Understanding algebraic expressions in financial contexts can transform theoretical problems into practical solutions.

Take our exercise, for instance. Knowing how much a creditor will receive based on a bankruptcy payout lets businesses and individuals gauge financial impacts.

Basics of financial literacy in algebra include:

• Understanding the concept of percentages and their calculations.
• Applying algebraic equations to financial scenarios.
• Assessing debts, repayments, and remaining balances.

Being financially literate means making informed decisions and applying logical steps, much like solving an algebraic equation. This knowledge helps people manage their finances more prudently and prepare for situations where debts cannot be fully repaid.