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(52781)   (Show Source):
You can put this solution on YOUR website! .
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.
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