Let's consider a real-world scenario involving savings and interest rates to model the equation \(0.08x = 0.06x + 140\).
Scenario:
Imagine that you are planning to save money in two different accounts. One account offers an interest rate of 8% per year, while the other account offers an interest rate of 6% per year. You have a total of \(x\) dollars that you are planning to invest.
You decide to invest part of your money in the first account (the 8% account) and the rest in the second account (the 6% account). After one year, the total interest earned from the first account equals the total interest earned from the second account plus an additional $140.
Mathematical Representation:
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The interest earned from the account with an 8% interest rate for the amount \(x\) is modeled as \(0.08x\).
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The interest earned from the account with a 6% interest rate for the amount \(x\) is modeled as \(0.06x\).
According to the problem, the total interest from the first account (8%) is equal to the total interest from the second account (6%) plus $140. This can be expressed as the equation:
\[ 0.08x = 0.06x + 140 \]
Conclusion:
In order to find how much money you have invested in both accounts or determine a specific amount to maximize your savings, you would solve the equation \(0.08x = 0.06x + 140\). This real-world problem captures the essence of the equation and provides a context for the financial situation it represents.
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