SOLUTION: The basic model of a particular car​ (2WD) with a power sunroof costs ​$27,485. When equipped with​ four-wheel drive​ (4WD) and a​ sunroof, the​

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: The basic model of a particular car​ (2WD) with a power sunroof costs ​$27,485. When equipped with​ four-wheel drive​ (4WD) and a​ sunroof, the​      Log On

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Question 1058411: The basic model of a particular car​ (2WD) with a power sunroof costs ​$27,485. When equipped with​ four-wheel drive​ (4WD) and a​ sunroof, the​ vehicle's price rose to ​$30,105. The cost of the basic model with 4WD was ​$29,405. Find the basic​ price, the cost of​ 4WD, and the cost of a sunroof.
Answer by ikleyn(52775) About Me  (Show Source):
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The basic model of a particular car (2WD) with a power sunroof costs $27,485. When equipped with four-wheel drive (4WD) and sunroof,
the vehicle's price rose to $30,105. The cost of the basic model with 4WD was $29,405.
Find the basic price, the cost of 4WD, and the cost of a sunroof.
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Let x = the cost of the basic model,
    y = the cost of 4DW,
    z = the cost of the sunroof.

Then you are given these three equations

x +     z = 27485,     (1)    ("The basic model of a particular car (2WD) with a power sunroof costs $27,485.")
x + y + z = 30105,     (2)    ("When equipped with four-wheel drive (4WD) and sunroof, the vehicle's price rose to $30,105.")
x + y     = 29405.     (3)    ("The cost of the basic model with 4WD was $29,405.")

The solution is very easy and straightforward.

First, distract the equation (1) from the equation (2). You instantly will get the solution for y: y = 30105 - 27485 = 2620.
Thus the cost of 4DW is $2620.

Next, distract the equation (3) from the equation (2). You instantly will get the solution for z: z = 30105 - 29405 = 700.
Thus the cost of the sunroof is $700.

By having this, you can now find x from any of the equations (1), (2) or (3).
For example, from (1) x = 27485 - z = 27485 - 700 = 26785.

Answer.  The basic models costs $26785. 4DW costs $2620.  The sunroof costs $700.

Solved.