Question 1067501: The basic model of a particular car (2WD) with a power sunroof costs $28,375. When equipped with four-wheel drive (4WD) and a sunroof, the vehicle's price rose to $30,955. The cost of the basic model with 4WD was $30,255. Find the basic price, the cost of 4WD, and the cost of a sunroof.
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
The basic model of a particular car (2WD) with a power sunroof costs $28,375.
When equipped with four-wheel drive (4WD) and sunroof, the vehicle's price rose to $30,955.
The cost of the basic model with 4WD was $30,255.
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 = 28375, (1) ("The basic model of a particular car (2WD) with a power sunroof costs $28375.")
x + y + z = 30955, (2) ("When equipped with four-wheel drive (4WD) and sunroof, the vehicle's price rose to $30955.")
x + y = 30255. (3) ("The cost of the basic model with 4WD was $30255.")
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 = 30955 - 28375 = 2580.
Thus the cost of 4DW is $2580.
Next, distract the equation (3) from the equation (2). You instantly will get the solution for z: z = 30955 - 30255 = 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 = 28375 - z = 28375 - 700 = 27675.
Answer. The basic models costs $27675. 4DW costs $2580. The sunroof costs $700.
Solved.
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