Question 1140468: A sports shop buys tents for $260 less 25% for buying more than 30 tents. The store operates on a markup of 30% of the sale price and advertises that all items are sold at a discount of 20% of the regular price. What is the regular price of the tents?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
from what i can see, the regular price can be anything, based on the information you provided.
let r = the regular price.
let s = the sale price
let m = the markup price.
let c = the cost price.
you state:
The store operates on a markup of 30% of the sale price and advertises that all items are sold at a discount of 20% of the regular price.
this makes:
m = 1.3 * s
s = .8 * r
this makes m = 1.3 * .8 * r = 1.04 * r
if we try to solve for r, we get r = m / 1.04
since m = 1.3 * s, then r = 1.3 * s / 1.04
since s = .8 * r, then r = 1.3 * .8 * r / 1.04
that becomes r = 1.04 * r / 1.04.
that becomes r = r.
that's an identity, which means that r can be anything.
i then decided to assume some values for r to see if it's true that r could be anything.
i first chose r = 5000.
assuming r = 5000, then s = .8 * r = .8 * 5000 = 4000
assuming m = 1.3 * s, then m = 1.3 * 4000 = 5200
assuming m = 1.04 * r, then m = 1.04 * 5000 = 5200
i then chose r = 1600.
assuming r = 1600, then s = .8 * 1600 = 1280
assuming m = 1.3 * s, then m = 1.3 * 1280 = 1664
assuming m = 1.04 * r, then m = 1.04 * 1600 = 1664
the actual cost of the tent doesn't even figure in this problem, since there's nothing that relates the regular price to the cost.
based on the information provided, i would have to say that the regular price could be anything, and the requirements of the problem would still be satisfied.
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