# A car normally depreciates 30% of its original value in the first year. A car is worth $11,466... ## Question: A car normally depreciates 30% of its original value in the first year. A car is worth$11,466 after the first year.

What was its original value?

Depreciation is defined as the loss in value of a fixed asset, such as a motor vehicle or furniture. Normally, the depreciation rate is stated in percentage terms. For example, if furniture depreciates at the rate of 10% per year and its value this year is $150, then the value of this asset in the next year will be 90% of its current value which is {eq}\dfrac{90}{100}\times \$150 = \$135 {/eq}. ## Answer and Explanation: Let the original value of the car be {eq}y {/eq}. If a car depreciates 30% of its original value in the first year, and the car is worth$11,466 after the first year, then this means that this value is 70% of the original value. Therefore:

• {eq}\dfrac{70}{100}x = \$11,466 {/eq} Solving for x: • {eq}x = \dfrac{\$11,466\times 100}{70} {/eq}
• {eq}x = \$16,380 {/eq} The original value of the car is {eq}\boxed{\color{blue}{\$16,380}} {/eq}