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Mathematical Problems and Solutions for Discounts, Markdowns, and Markups

## Arrow Manufacturing

1.    Arrow Manufacturing offers discounts of 20%, 11.5%, 66% on a line of products. For how much should an item be listed if it is to be sold for \$ 172.41?

The item should be listed for \$ ?

2.      Jewellers sells diamond necklaces for \$463.00 less 8%. Starlight                     Jewellers offers the same necklace for \$ 592.00 less 26 %, 12 % What additional rate of         discount must     Shamin offer to meet the competitor's price?

The additional rate of discount that Shamin Jewellers must offer to meet the             competitor's price is

3.    Guiseppe's buys supplies to make pizzas at a cost of \$4.73. Operating expenses of the         business are 144% of the cost and the profit he makes is 182% of cost. What is the         regular selling price of each pizza?

The regular selling price of each pizza is

4.    What amount must be remitted if the following invoices, all with terms 5/10, 2/30, n/60,         are paid together on December 8?

Invoice No. 312 dated November 2 for \$923.00
Invoice No. 429 dated November 14 for \$784.00
Invoice No. 563 dated November 30 for \$873.00

The amount remitted is

5.    Par Putters Company sells golf balls for \$32 per dozen. The store's overhead             expenses are 44 % of cost and the owners require a profit of 23 %of cost.

(a) For how much does Par Putters Company buy one dozen golf balls?
(b) What is the price needed to cover all of the costs and expenses?
(c) What is the highest rate of markdown at which the store will still break even?

(a) The cost of one dozen golf balls is

(Round the final answer to two decimal places as needed. Round all intermediate values     to six decimal places as needed.)

(b) The price needed to cover all of the costs and expenses is

(Round the final answer to two decimal places as needed. Round all intermediate values     to six decimal places as needed.)

(c) The highest rate of markdown is

(Round the final answer to two decimal places as needed. Round all intermediate values     to six decimal places as needed.)

6.    A department store paid \$54.08 for a cookware set. Overhead expense is 18 % of the         regular selling price and profit is 18 % of the regular selling price. During a clearance         sale, the set was sold at a markdown of 30 %. What was the operating profit or loss on         the sale?

Profit or loss?

Was \$ ?

(Round the final answer to the nearest cent as needed. Round all intermediate values to         six decimal places as needed.)

7.    Aldo's ShoesAldo's Shoes bought a shipment of 632 pairs of women's shoes for \$48.00         per pair. The store sold 134 pairs at the regular selling price of \$ 143.00 per pair, 58         pairs at a clearance sale at a discount of 41 %, and the remaining pairs during an         inventory sale at a price that equals cost plus overhead. The store's overhead is 29 % of         cost.

(a) What was the price at which the shoes were sold during the clearance sale?
(b) What was the selling price during the inventory sale?
(c) What was the total profit realized on the shipment?
(d) What was the average rate of markup based on cost that was realized on the             shipment?

(Round the final answer to two decimal places as needed. Round all intermediate values     to six decimal places as needed.)

8.    A jewellery store paid a unit price of \$250 less 40%, 16 and two thirds %, 8%
for a shipment of designer watches. The store's overhead is 65% of cost and the normal         profit is 55% of cost.

(a) What is the regular selling price of the watches?
(b) What must the sale price be for the store to break even?
(c) What is the rate of markdown to sell the watches at the break-even price?

9.     What amount will reduce the amount due on an invoice of \$3133.55 by \$ 976.23 if the         terms of the invoice are 44/15, n/30 and the payment was made during the             discount period

The payment amount is

(Round the final answer to the nearest cent as needed. Round all intermediate values to         six decimal places as needed.)

10.    A merchant realizes a markup of \$42 by selling an item at a markup of 37.5% of cost.         The merchant's overhead expenses are 17.5% of the regular selling price. At a             promotional sale, the item was reduced in price to \$121.66.
(a) What is the regular selling price?
(b) What is the rate of markup based on the regular selling price?
(c) What is the rate of markdown?
(d) What is the profit or loss during the promotional sale?

(a) The regular selling price is

(Round to the nearest cent as needed.)

(b) The rate of markup based on selling price is

(Round to two decimal places as needed.)

(c) The rate of markdown is