For a special sale, a mens tie buyer plans to promote a $39.99 tie. Consequently, the buyer purchases 450 ties and wants to achieve a 55% markup. An order for 100 ties that cost $20.00 each is also placed by this same buyer. What will be the average cost of the remaining pieces (Show two decimal places)?

Answer:The average cost of each tie is $56.350Step-by-step explanation:We are given that a men tie buyer plans to promote a $39.99 tie. Consequently, the buyer purchases 450 ties So, Cost of 450 ties = [tex]450 \times 39.99=17995.5[/tex]An order for 100 ties that cost $20.00 eachCost of 100 ties = [tex]100 \times 20 = 2000[/tex]Total cost price = 17995.5+2000 = 19995.5Let the selling price of 1 tie be xTotal ties = 450+100 = 550So, SP of 550 ties =550xNow we are given that markup is 55%So, Profit % = 55%So, [tex]CP = \frac{SP \times 100}{100+P\%}[/tex]Substitute the values [tex]19995.5 = \frac{550x \times 100}{100+55}[/tex][tex]19995.5 = \frac{550x \times 100}{155}[/tex][tex]19995.5 \times 155 = 55000x[/tex][tex]\frac{19995.5 \times 155}{55000}=x[/tex][tex]56.350=x[/tex]Hence The average cost of each tie is $56.350