SOLUTION: Hi 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 c

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Question 1208330: Hi
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.
Found 4 solutions by greenestamps, ikleyn, math_tutor2020, MathTherapy:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


He makes a $135 profit if he sells at a 15% discount of the marked price; he has a loss of $65 if he sells at a 25% discount.

A profit of $135 compared to a loss of $65 represents a change of $200 in the selling price.

That change of $200 results from the additional 10% discount, so 100% of the marked price is $2000.

With a discount of 15% of the marked price, the selling price is 85% of $2000, which is $1700.

He makes a profit of $135 if he sells at a 15% discount, so his cost was $1700-$135 = $1565.

ANSWER: $1565

To check the answer, see that the selling price with a discount of 25% is 75% of $2000, which is $1500; that is $1565-$1500 = $65 less than his cost, giving him a loss of $65.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~


        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. 


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. 

    
ANSWER.  The cost price is $1565.

Solved.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = cost price = amount Bob paid for the TV
y = marked price = amount that Bob's customer pays if no discounts are applied

0.15y = amount the customer saves if 15% discount is applied
y - 0.15y = 0.85y = amount the customer pays after the 15% discount
0.85y-x = profit Bob makes = 135
0.85y-x = 135
x = 0.85y-135
We'll use this later.

0.25y = amount the customer saves if 25% discount is applied
y - 0.25y = 0.75y = amount the customer pays after the 25% discount
0.75y-x = profit Bob makes = -65
0.75y-x = -65
0.75y-(x) = -65
0.75y-(0.85y-135) = -65 ....... plug in x = 0.85y-135
0.75y-0.85y+135 = -65
-0.10y+135 = -65
-0.10y = -65-135
-0.10y = -200
y = -200/(-0.10)
y = 2000
This is the amount the customer would pay if no discounts are applied.

Then,
x = 0.85y-135
x = 0.85*2000-135
x = 1565 dollars is the cost price of the TV.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Hi
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. 

Let marked price be P, and cost price, C

A discount of 15% off of the marked price means that it'd be sold for 100% - 15% = 85% of the marked price, or .85P
Since a discount of 15% off of the marked price yields a PROFIT of $135, we get: .85P = C + 135 ----- eq (i)

A discount of 25% off of the marked price means that it'd be sold for 100% - 25% = 75% of the marked price, or .75P
Since a discount of 25% off of the marked price yields a LOSS of $65, we get: .75P = C - 65 ------ eq (ii)

               .85P = C + 135 ----- eq (i)
               .75P = C - 65 ------ eq (ii)
                .1P = 200 ----- Subtracting eq (ii) from eq (i) 
Marked price, or 

         .75(2,000) = C - 65 ----- Substituting 2,000 for P in eq (ii)
              1,500 = C - 65
         1,500 + 65 = C 
            $1,565 = C (Cost)
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