Explanation Given Information: An American-made car depreciates 25% of its original cost in first year and 14% of its remaining in the second year, the original cost of the car is $36,400, $28,400 and $26,800. Formula used: The steps to solve the problem: 1. Familiarize the problem situation. 2. Translate the problem to an equation. 3. Solve the equation. 4. Check the answer in the original problem. 5. State the answer to the problem clearly. Also, for any variable a, x % of a is: x % × a = x 100 × a Calculations: To solve this problem, consider the 5 steps given below: Familiarize An American-made car depreciates 25% of its original cost in first year and 14% of its remaining in the second year, the original cost of the car is $36,400 $36,400, $28,400 and $26,800. Let the value at the end of first year be Y. Translate For the original cost of car as $36,400. Hence, a = 36 , 400 and x = 25 % Substitute a = 36 , 400 and x = 25 % in x % × a = x 100 × a to get the depreciation as: Thus: 25 % × 36400 = 25 100 × 36400 Solve: To solve the equation, carry out the operations: 25 % × 36400 = 25 100 × 36400 = 36400 4 = 9100 The value at the end of first year is: Y = 36 , 400 − 9100 = $ 27 , 300 Similarly, the depreciation for second year is calculated by substitution of a = 27300 and x = 14 % in x % × a = x 100 × a as: 14 % × 27300 = 14 100 × 27300 = 14 × 273 = 3822 The value of the car after second year will be: Y = 27 , 300 − 3 , 822 = 23 , 478 Step 4: Check Add the depreciations of two years to final value to get initial value as: 23478 + 3822 + 9100 = ? 36400 36400 = ? 36400 Thus, the answer is checked. Step 5: State Hence, the final value after two years is $23,478. For the original cost of car as $28,400. Familiarize An American-made car depreciates 25% of its original cost in first year and 14% of its remaining in the second year, the original cost of the car is $28,400. Let the value at the end of first year be Y. Translate Since the original cost of car is $28,400

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 4.6, Problem 10ES

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To calculate: The value of the American made car at the end of second year if the initial value is $36,400, $28,400 and $26,800.

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Chapter 4.6, Problem 9ES

Chapter 4.6, Problem 11ES

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Chapter 4 Solutions

Developmental Mathematics (9th Edition)

Ch. 4.1 - Objective 2.1e: Simplify fraction...Ch. 4.1 - Prob. 2SR Ch. 4.1 - Prob. 1DE Ch. 4.1 - Prob. 2DE Ch. 4.1 - Prob. 3DE Ch. 4.1 - Prob. 4DE Ch. 4.1 - Prob. 5DE Ch. 4.1 - Prob. 6DE Ch. 4.1 - Prob. 7DE Ch. 4.1 - Prob. 8DE

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The value of the American made car at the end of second year if the initial value is $36,400, $28,400 and $26,800.

Solution Summary: The author calculates the value of the American-made car at the end of second year at 36,400, 28,400 and 26,800 respectively.

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To calculate: The value of the American made car at the end of second year if the initial value is $36,400, $28,400 and $26,800.

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Chapter 4 Solutions