Orlando bought a new couch for $2,736, using the furniture store's finance plan. He will pay $114 a month for 24 months. Which equation can be used to find y, the amount Orlando still owes after each month of the plan?
A. [tex]y=114 x-2,736[/tex]
B. [tex]y=2736-114 x[/tex]
C. [tex]y=114 x[/tex]
D. [tex]y=2,736+114 x[/tex]
Answer (2)
Define the variables: y is the amount owed, and x is the number of months.
Start with the initial amount owed: $2 , 736 .
Subtract the monthly payments: $114 per month.
The equation is: y = 2736 − 114 x .
Explanation
Problem Analysis Let's analyze the problem. Orlando bought a couch for $2 , 736 and pays $114 each month. We need to find an equation that represents the amount he still owes after x months.
Equation Setup Let y be the amount Orlando still owes after x months. The initial amount he owes is $2 , 736 . Each month, he pays $114 , so the amount he owes decreases by $114 x . Therefore, the equation is: y = 2736 − 114 x
Final Equation The equation that represents the amount Orlando still owes after each month is y = 2736 − 114 x .
Examples
Understanding how loans and debts decrease over time is crucial in personal finance. For instance, if you borrow money to buy a car or a house, this type of equation helps you calculate how much you still owe each month. By tracking the remaining balance, you can plan your budget effectively and ensure you're on track to pay off your debt. This also helps in comparing different loan options to see which one allows you to pay off the debt faster.
The equation representing the amount Orlando still owes after each month is y = 2736 − 114 x . This indicates he begins with $2,736 and pays off $114 each month. Therefore, after x months, the amount remaining decreases accordingly.
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