Question 1208330
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If Bob sells a TV at a discount of 15% of the marked price he will make a profit of $135. 
If he sells at a discount of 25% of marked price he makes a loss of $65. 
What is the cost price of the TV.
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        By the definition,  " cost price "  is the amount of money that is spent to produce  

        goods or services before any profit is added for the manufacturer or producer.



<pre>
Let X be the cost price in this problem.

Let Y be the selling price in this problem (same as the marked price).


From the first statement of the problem, we have this equation

    (1-0.15)Y - X = 135  dollars   (1)     (profit)


From the second statement of this problem, we have second equation

    (1-0.25)Y - X = -65  dollars    (2)    (loss)


So, we have a system of two equations, which I will write in the form

    0.85Y - X = 135    (1')

    0.75Y - X = -65    (2')


To solve it, subtract equation (2') from equation (1').  You will get

    0.85Y - 0,75Y = 135 - (-65),

    0.1Y = 200,

       Y = 200/0.1 = 2000.


To find X, substitute Y = 2000 into equation (1')

    0.85*2000 - X = 135,

    0.85*2000 - 135 = X,

          1565      = X,

             X      = 1565. 

    
<U>ANSWER</U>.  The cost price is $1565.
</pre>

Solved.