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(13198)   (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(52776)  (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.
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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.
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(3816)  (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(10551)  (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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