SOLUTION: 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 discou

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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