Math Problem Statement
Suppose a car with an initial value of $25400 depreciates by $820 every year. Set up an equation that answers the the question: How long will it take for the value of the car to decrease to $7500? Use y as your variable.
Solution
To find out how long it will take for the value of the car to decrease to $7500, we need to set up a linear equation based on the given depreciation information.
We know:
- The car’s initial value is $25,400.
- The car depreciates by $820 each year.
- We are looking for when the value of the car will be $7,500.
Let represent the number of years it takes for the car to depreciate to $7,500.
Equation setup:
The value of the car decreases by $820 each year, so after years, the car’s value is:
We want the car's value to be $7,500, so we set the equation equal to $7,500:
Solve for :
-
Subtract 7,500 from both sides:
-
Divide both sides by 820:
So, it will take approximately 21.83 years (about 21 years and 10 months) for the car's value to decrease to $7,500.
Would you like more details on how we solved this?
Related questions:
- What would be the value of the car after 10 years?
- How long will it take for the car's value to drop to half of its initial value?
- How much is the car worth after 5 years?
- If the annual depreciation increases to $1,000, how many years would it take to reach $7,500?
- What is the value of the car after 15 years?
Tip: Linear depreciation means the car's value decreases by the same amount each year, creating a straightforward way to calculate future values.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Depreciation
Algebra
Formulas
Car's value after y years: 25400 - 820y
Solving linear equation: 25400 - 820y = 7500
Theorems
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Suitable Grade Level
Grades 8-10
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