# You buy 3,000 pairs of sunglasses at the beginning of the summer. You estimate that 20 percent of them will have to be put on your "bargain table" at the end of the season on which everything is priced at \$1.00.  Generally, about thirty percent of the "bargain table" items will be damaged or broken and will have to be thrown away. The glasses cost you  \$1.25 per pair and you want an average markup of 36% based on selling price. Round your final answer properly to two decimal places. a)  What is the total cost (TC)? \$  ____________  b)  What is the total sales (TS) given the total cost (TC) and the average mark up (TM)? \$  ____________  c)  At what price must they start selling the sunglasses? \$  ____________

a) There are 3000 pairs of sunglasses and each was bought at \$1.25

Total cost is:

`TC =3000*\$1.25 =\$3750.00`

Thus the total cost is \$3750

b) The average markup is 36%, from the total cost and is the difference between the total selling price and the total cost.

`TM =...

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a) There are 3000 pairs of sunglasses and each was bought at \$1.25

Total cost is:

`TC =3000*\$1.25 =\$3750.00`

Thus the total cost is \$3750

b) The average markup is 36%, from the total cost and is the difference between the total selling price and the total cost.

`TM = TS -TC `

`TS = TM+TC =36%*TC +TC =0.36*TC+TC =1.36*TC `

`TS =1.36*\$3750.00 =\$5100.00`

Hence the total sales are \$5100

c)

On the "bargain table" there will be 20% of 3000 pairs of glasses. It means

`20%*3000 =0.2*3000 =600`  pairs of glasses

From these 600 pairs 30% will be thrown away as being damaged.

`30%*600 =0.3*600 =180`  pairs thrown.

The remaining pairs will be sold with \$1.00 The selling price for these will be

`S =(600-180)*\$1 =\$420.00`

The total number of glasses to be sold at initial price is

`3000-600 =2400` pairs of glasses

The total price to sell the initial 2400 pairs of glasses is

`Si= TS-S =\$5100.00-\$420.00 =\$4680.00`

The initial price for one pair is

`P =(\$4680.00)/2400 =\$1.95`

They need to start selling the sunglasses at \$1.95 per pair

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