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Question 307076: Store A sells a product with a 15% discount and an additional $90 off of the list price. Store B sells the same product at a 25% discount with no additional discount. After all discounts, the price at Store A is $15 less than at Store B. What is the list price for the product at Store A?
Here is what I have so far. I don't know if I am on the right track, or where to go from here. Thanks.
A = x - (0.15 * x) - 90
B = y - (0.25 * y)
A = B - 15
x - (0.15 * x) - 90 = y - (0.25 * y) - 15
0.85x - 75 = 0.75y
(now what?)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! You're on the right track.
Usually the list price for the product is the same all over and the stores compete on sale price.
Here, it looks like they are implying that the list price is different for both stores.
If they were the same, your answer would have been simple.
Your equations would have been:
A = x - (0.15 * x) - 90
B = x - (0.25 * x)
A = B - 15
x - (0.15 * x) - 90 = x - (0.25 * x) - 15
0.85x - 75 = 0.75x
You would get:
A = x - (0.15 * x) - 90
B = y - (0.25 * x)
A = B - 15
x - (0.15 * x) - 90 = x - (0.25 * x) - 15
0.85x - 75 = 0.75x
.10x = 75
x = 750
The list price of the item would have been $750.
A would then equal 750 - .15*750 - 90 = 547.5
B would then equal 750 - .25*750 = 562.5
562.5 - 547.5 = 15 which makes A equal to $15.00 less than B.
Since they are different, you have correctly gotten to the point of your final equation as shown below:
A = x - (0.15 * x) - 90
B = y - (0.25 * y)
A = B - 15
x - (0.15 * x) - 90 = y - (0.25 * y) - 15
0.85x - 75 = 0.75y
Since you were looking for the list price at store A, you would have had to solve for x to get:
0.85x - 75 = 0.75y becomes:
.85x = .75y + 75 which becomes:
x = (.75y + 75)/.85 which becomes:
x = .75y/.85 + 75/.85 which becomes:
x = .882352941*y + 88.23529412
This would be the best you could do because the value of x would depend on the value of y.
Assuming y was $1000, then x would have had to be:
.882352941*1000 + 88.23529412 = 970.5882353
You would have had:
x = 970..5882353 and y = 1000.
Plugging these values into the original equations, you would have gotten:
A = .85*x - 90 = 735
B = .75*y = 750
A would have been $15.00 less than B as required.
If you pick any other value for y, you should come up with the same difference.
Example:
Let y = 350.
This makes x = 397.0588235 and y = 350.
A = .85*x - 90 = 247.5
B = .75*y = 262.5
B - A = 262.5 - 247.5 = 15
Sale price of A is 15.00 less than B.
You can get an answer of x in relation to y, but you can't fix the solution on one value of y.
y can be any value.
I suspect the list price of the item at both stores should have been the same, but, if not, then your answer would have to be:
x = .882352941*y + 88.23529412
In fractional terms that would be:
x = (.75/.85)*y + (75/.85)
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