The principal's new car cost $35,000, but in three years it will only be worth $21,494. Write an equation for this situation and explain what each part of the equation represents in the context of the problem. What is the annual rate of depreciation?

Question

The principal's new car cost  $35,000, but in three years it will only be worth  $21,494. Write an equation for this situation and explain what each part of the equation represents in the context of the problem. What is the annual rate of depreciation?

Bytelearn · Accepted Answer

Denote Equations: Let's denote the original cost of the car as $ C_0 $, the value of the car after three years as $ C_3 $, and the annual rate of depreciation as $ r $. We can write the equation for the depreciation of the car over three years as: $$ C_3 = C_0 - 3r $$ In this equation, $ C_0 $ represents the initial cost of the car, $ C_3 $ represents the value of the car after three years, and $ 3r $ represents the total depreciation over three years.Plug in Values: Now we can plug in the values we know into the equation: $$ 21494 = 35000 - 3r $$ This equation will allow us to solve for $ r $, the annual rate of depreciation.Isolate and Solve: To find $ r $, we need to isolate it on one side of the equation. We'll start by adding $ 3r $ to both sides and then subtracting $ 21494 $ from both sides: $$ 3r = 35000 - 21494 $$Calculate Difference: Next, we calculate the difference on the right side of the equation: $$ 3r = 13506 $$Divide and Find Rate: Now, we divide both sides by 3 to find the annual rate of depreciation: $$ r = \frac{13506}{3} $$Performing the division gives us: $$ r = 4502 $$ So, the annual rate of depreciation is $4502.

The principal's new car cost $\$ 35,000$ , but in three years it will only be worth $\$ 21,494$ . Write an equation for this situation and explain what each part of the equation represents in the context of the problem. What is the annual rate of depreciation?

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The principal's new car cost $35,000 \$ 35,000 $35,000, but in three years it will only be worth $21,494 \$ 21,494 $21,494. Write an equation for this situation and explain what each part of the equation represents in the context of the problem. What is the annual rate of depreciation?

The principal's new car cost $\$ 35,000$ , but in three years it will only be worth $\$ 21,494$ . Write an equation for this situation and explain what each part of the equation represents in the context of the problem. What is the annual rate of depreciation?