Credit Cards. A couple stopped using their VISA credit...

Credit Cards. $\quad$ A couple stopped using their VISA credit card charging $1.5 \%$ per month interest and their Robinsons-May credit card charging $1.75 \%$ per month interest because they had built up a combined debt of $\$ 16,500$ on the two cards. For one month, they made no purchases or payments on the accounts. If the total amount of interest the credit cards accumulated during the month was $\$ 259.25,$ what amount did they owe on each card when they stopped using them?

Key Concepts

Systems of Linear Equations

When dealing with multiple financial instruments or accounts, each with their own rates and balances, the problem often involves setting up and solving systems of linear equations. This method uses multiple equations to represent the relationships between different quantities, such as total debt and total interest accrued, and is a powerful tool for determining individual balances when given aggregate totals.

Simple Interest Calculation

This concept involves computing interest as a percentage of the principal over a certain period. In the context of credit cards, the monthly interest is typically calculated by multiplying the outstanding balance by the monthly interest rate. It is a foundational idea in financial mathematics that helps in understanding how debts and investments grow over time.

Percentages in Financial Calculations

Percentages are used to express interest rates, fees, and proportions in finance. They allow for the easy conversion of rates and comparisons across different scenarios. In problems involving multiple interest rates, percentages are crucial for accurately determining the contribution of each rate to the overall cost, such as in calculating the accumulated interest on different credit card balances.

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