SOLUTION: A buyer of tv sets wishes to maintain a markup of 37 1/2% after all mark-downs are taken. Of 25 sets costing $150 each, he sells 20 at $265. How much can he mark-down the remainin

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Question 226393: A buyer of tv sets wishes to maintain a markup of 37 1/2% after all mark-downs are taken. Of 25 sets costing $150 each, he sells 20 at $265.
How much can he mark-down the remaining 5 sets and still realize his mark-up objective?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
25 sets cost $150 apiece.

markup of 37.5% would be 150 + .375*150 = 150 +56.25 = 206.25

he needs to collect 25 * 206.25 to get the 37.5% markup on all the tv sets he sells.

25 * 206.25 means he needs to collect 5156.25

25 * 150 means the total cost to him was 3750

5156.25 / 3750 = 1.375 - 1 = .375 * 100% = 37.5%

He sold 20 at $265 apiece meaning he collected 20 * 265 = 5300.

He needs to collect 5156.25 minus 5300 to exactly equal his 37.5% markup.

5156.25 minus 5300 = -143.75 / 5 = -28.75.

This means he can give the remaining 5 sets away plus give each person an additional $28.75 in order to realize his original markup.

His cost for the set is $150.
He gives it away plus an addition $28.75.

His markdown is $150 plus $28.75 equals $178.75 / $150.00 = 1.11916666667 * the original price equals 111.9166666667%.

Here's how that would work.

Original cost is $150 * 25 = $3750.
Needs to make ($150 + .375*150) * 25 = 206.25 * 25 = $5156.25
Sold 20 at $265 = $5300.00
Gave away 5 plus $28.75 = -$143.75

Add $5300 and -$143.75 to get $5156.25

Markdown on the remaining 5 is 111.9166666667%

He made too much money on the original 20.

He can give the remaining sets away and still realize more than he wanted to make in the first place.

Formula to use would be:

(20 * 265) + (5 * x) = 25 * 150 * 1.375

This becomes:

5300 + 5x = 5156.25

This becomes:

5x = 5156.25 - 5300 = 143.75

This becomes:

x = - $28.75

Markdown is Sale price minus cost, divided by cost.
Markdown is therefore -$28.75 - $150 = -$178.75 / $150 = - -1.19166666667 * 100% equals -111.9166666667 percent.

Numbers look a little odd but that's the way it works out.