To create a real-world problem that models the equation \( 0.08x = 0.06x + 140 \), we can consider a scenario involving savings and interest rates.
Real-World Problem:
Sarah is saving money for a vacation. She has two different savings accounts.
- The first account offers an interest rate of 8% per year. Let's say Sarah invests \( x \) dollars in this account.
- The second account offers an interest rate of 6% per year. She also has some money, amounting to $140, already earning the lower interest rate, but she decides to invest \( x \) dollars from her first account in this second account.
At the end of the year, the amount of interest Sarah earns from both accounts will be the same.
Set up the equation based on the situation:
- The interest earned from the first account after one year is \( 0.08x \).
- The interest earned from the second account (from the $140 and the \( x \) dollars invested) is \( 0.06x + 140 \).
Now, we can model this situation with the equation:
\[ 0.08x = 0.06x + 140 \]
By solving this equation, Sarah can figure out how much money she should invest to ensure that the interest from both accounts is equal.
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