Deck 4: Mathematics of Merchandising

Question 1

The net proceeds to the vendor of a house after payment of a 5.5% real estate commission were $160,555.50. At what price did the house sell?

Answer 1

$169,900

Question 2

Mr. and Mrs. Ogrodnik want to list their house at a price that will net them a minimum of $320,000 after a real estate commission of 5.5% of the selling price. Rounded to the nearest $100, what is the lowest offer they could accept on their home?

Answer 2

$338,600

Question 3

After a trade discount of 27.5%, a jeweller can obtain ahalf carot Canadian Polar Bear diamonds for $2,138.75. What is the dollar amount of the trade discount?

Answer 3

$811.25

Question 4

Niagara Dairies gives convenience stores a trade discount of 24% on butter listed at $72.00 per case. What rate of discount will Silverwood Milk Products have to give on its list price of $74.50 per case to match Niagara's price to convenience stores?

Question 5

A 37.5% trade discount on a camera represents a discount of $223.14 from the suggested retail price. What is the net price to the buyer?

Question 6

Specialty Builders Supply has two sources for the same power saw. Source A sells the saw at $196.00 less 20%, and Source B offers it at $186.60 less 16 %. Which source is less expensive?

Question 7

A 28% trade discount on a personal video recorder represents a discount of $136.92 from the suggested retail price. What is the net price to the buyer?

Question 8

Specialty Builders Supply has two sources for the same power saw. Source A sells the saw at $196.00 less 20%, and Source B offers it at $186.60 less 16 %. Which source is less expensive?

Question 9

Best Buy Entertainment can obtain Panasonic Blu-ray players for $134 less a trade discount of 35%. A comparable Samsung model is available for $127 less a discount of 30%. Which DVD player has the lower net cost? How much lower?

Question 10

Cynthia and Byron sell mutual funds for Syndicated Investors. Purchasers of mutual funds from agents of Syndicated Investors pay a front-end commission of 5.5%. The commission is paid on the total amount paid to Syndicated Investors, not on just the net amount actually invested in mutual funds.
a) Mr. and Mrs. Stevens placed $5,500 through Cynthia. What (net) amount was actually invested in mutual funds after the commission was paid?
b) If the net amount invested in mutual funds as a result of Byron's sale to Mrs. Stocker was $6,426, what (dollar) amount of commission was paid on the sale?

Question 11

The net proceeds to the vendor of a house after payment of a 4.5% real estate commission were $275,995. At what price did the house sell?

Question 12

A trade discount of 22.5% from the suggested selling price for a line of personal computers translates to a $337.05 discount. What net price will a retailer pay?

Question 13

A college bookstore buys back good-condition textbooks for 45% off the retail price of new books. What will a student receive for a book currently selling at $104.50 new?

Question 14

In three successive years the price of the common shares of Bedrock Resources Ltd. fell 40%, 60%, and 70%, ending the third year at 50 cents.
a) What was the share price at the beginning of the three-year skid?
b) How much (in dollars and cents) did the share price drop in the second year?

Question 15

Net price to a car dealer of a model with a manufacturer's list price of $34,900 is $28,687.80. What trade discount rate is the dealer being given?

Question 16

A merchant pays a 3.5% fee to the BMO Bank of Montreal on all MasterCard sales.
a) What amount will she pay on sales of $17,564 for a month?
b) What were her gross sales for a month in which the bank charged total fees of $732.88?

Question 17

A merchant pays a 2.9% fee to the Royal Bank on all Visa sales.
a) What amount will he pay on sales for a month of $28,476?
b) What were his gross sales for a month in which the bank charged fees totalling $981.71?

Question 18

The distributor of Nikita power tools is offering a trade discount of 38% to hardware stores. What will be their cost to purchase a rotary saw listed at $135?

Question 19

Green Thumb Nursery sells spreading junipers to the gardening departments of local grocery and building supply stores. The net price per tree is $27.06 after a trade discount of $22.14. What rate of trade discount is the nursery giving to retailers?

Question 20

The net price of an item after a discount of 22% is $155.61. What is the (dollar) amount of the discount?

Question 21

In addition to the basic trade discount of 20%, an outboard motor manufacturer gives a boat dealer an additional discount of 12.5% for providing follow-up warranty service, and a 5% discount for cooperative advertising and boat-show promotions.
a) After the basic trade discount, what further price reduction (in dollars) does the 12.5% discount represent on a $1,000 list price motor?
b) After the first two discounts, what price reduction does the 5% discount give on the $1,000 motor?

Question 22

What total amount must be paid on May 4 to settle invoices dated April 20 for $650, April 24 for $790, and April 30 for $465, all with terms 1½/10, n/30?

Question 23

On May 25, Morris Hardware received an invoice from Precision Tools Inc. for $5,076.64. The invoice was dated May 22 and offered terms of 2/10, 1/20, n/30. What payment will settle the invoice on:
a) June 1?
b) June 2?
c) June 5?

Question 24

An invoice shows a net price of $199.16 after discounts of 22%, 7%, and 5% are deducted.
a) What was the list price of the goods?
b) What single discount would be equivalent to the discount series?

Question 25

A wholesaler lists an item for $48.75 less 20%. What additional "special promotion" discount must be offered to retailers to get the net price down to $36.66?

Question 26

The representative for a European ski manufacturer offers Snow 'n Surf Sporting Goods a regular discount of 25%, a volume discount of 10% for an order of at least 100 pairs of skis, and an early booking discount of 5% for orders placed before July 1.
a) If Snow 'n Surf is eligible for all three discounts on skis listed at a suggested retail price of $890, what is the net price per pair of skis?
b) Assuming that Snow 'n Surf qualifies for the volume discount, what is the dollar amount of the early-order discount per pair of skis?
c) The net price after all three discounts on a less expensive model of skis is $410.40. What is the suggested retail price?
d) What single trade discount rate would be equivalent to the three trade discounts?

Question 27

In addition to the regular trade discount of 25% and a volume purchase discount of 8 % from the manufacturer, Appliance Warehouse is offered a further 5% discount for orders placed in January.
a) What is the net price after all three discounts on refrigerators listed at $1,195?
b) What is the list price on an electric range whose net price works out to be $470.25?
c) What single trade discount is equivalent to the three trade discounts?
d) After the regular and volume discounts are both taken, what dollar amount of savings does the extra discount for January orders represent on a $1,000 list price item?

Question 28

The evening news reports that the S&P/TSX Index dropped 0.9% on the day to close at 13,123 points. How many points did the index fall?

Question 29

Ristorante Italiano made payments of $5,000 on March 29 and $3,000 on April 7 to General
Restaurant Supplies on an invoice for $11,870. The invoice was dated March 21 and carried terms of 1½/10, ½/20, n/30.
a) What is the balance after the second payment?
b) On what date is the balance due?

Question 30

At its current price of $1.10 per share, the price of Apex Resources stock is down 78% from its price 1 year ago. What was that price?

Question 31

An invoice shows a net price of $176.72 after trade discounts of 30%, 10%, and 2% have been deducted.
a) What was the list price of the goods?
b) What single discount would be equivalent to the discount series?

Question 32

White's Photography received an e-invoice from Fuji Canada dated February 27 of a leap year. The amount of the invoice is $2,896.77 with terms , 1/30, n/60.
a) What is the last date on which White's is eligible for the 2 % discount?
b) What amount will be required on that date to settle the invoice?
c) Instead of the payment in (b), what amount must be paid on March 29 to settle the invoice?

Question 33

a) Mirabai's income tax rate on additional income is 42%. She has just received a wage increase of $1.25 per hour. What is her after-tax increase in hourly pay?
b) Shira's tax rate on additional income is 47%. How much extra must he earn to keep an additional $1,000 after tax?

Question 34

The evening news reports that the S&P/TSX Composite Index dropped 1.7% on the day to close at 13,646 points. Rounded to the nearest integer, how many points did the index fall on the day?

Question 35

Ever-rest sells its mattresses for $960 less 25%. Posture-Perfect mattresses are listed at $880 less 20% and 5%. What second discount would Ever-rest need to offer to match Posture-Perfect's net price?

Question 36

Determine the payment required to settle the invoice on the indicated payment date:

Question 37

A retailer is offered a regular discount of 25%, a further discount of 7.5% if she places an order exceeding $10,000 (at list prices), and another 5% promotional allowance (discount) for participating in a joint promotion with the distributor.
a) If the retailer is eligible for all three discounts, what will be the net price of an order totalling $11,500?
b) What is the dollar amount of the saving from the quantity discount (assuming that she does not participate in the joint promotion)?
c) What is the dollar amount of the promotional allowance?

Question 38

Mapleview Poultry Farms gives convenience stores a discount of 25% on eggs listed at $43.00 per case. What trade discount will Sunnyside Farms have to give on its list price of $44.50 per case to match Mapleview's price to convenience stores?

Question 39

A uranium mining town reported population declines of 3.2%, 5.2%, and 4.7% for the three successive 5-year periods 1985-89, 1990-94, and 1995-99. If the population at the end of 1999 was 9,320:
a) How many lived in the town at the beginning of 1985?
b) What was the population loss in each of the 5-year periods?

Question 40

At its current price of $0.80 per share, the wholesale price of a commodity stock is down 73% from its price one year ago. What was that price?

Question 41

Given the following: Determine:
a) The amount of mark-up.
b) The amount of operating (overhead) expenses.
c) The operating profit or loss.
d) The rate of mark-up on cost.
e) The rate of mark-up on selling price.

Question 42

Northern Outfitters' invoice to Rico's Menswear for $2,463.80 was dated October 22 with terms 2/10, n/30. Late payments are charged a 1% penalty on the overdue balance. Rico made payments of $1,000 on October 31 and $800 on November 20. What amount will pay off the balance on December 8?

Question 43

Is it possible for the rate of mark-up on cost to exceed 100%?

Question 44

What total amount must be paid on July 4 to settle invoices dated June 20 for $485, June 24 for $367, and June 30 for $722, all with terms 1½/10, n/30?

Question 45

Loblaws purchases raisins at $85.75 per 25-kg box and then sells them in its bulk foods department for $0.59 per 100 g. What is Loblaws rate of mark-up on cost and rate of mark-up on selling price of the raisins?

Question 46

Mayfair Distributors sent Bed 'n Bath an invoice dated December 23 for $5,344.90 with terms 2/10, 1/20, n/30. The penalty on overdue accounts is 1½% of the overdue balance.
a) What is the balance after a payment of $3,000 on January 3?
b) What additional payment on January 30 will settle the account?

Question 47

Omega Restaurant buys Shiraz wine at $16.95 per bottle, and sells it to customers at $34.95 per bottle. Calculate Omega's rate of mark-up on cost and rate of mark-up on selling price of the wine.

Question 48

Ballard Jewellers received an invoice dated August 22 from Safeguard Security Systems for $2,856.57 with terms 2½/10, 1/20, n/45. Ballard made payments of $900 on September 1, $850 on September 10, and $700 on September 30. What amount was still owed on October 1?

Question 49

Omega Restaurant received an invoice dated July 22 from Industrial Kitchen Equipment for $3691, with terms 2/10, 1/20, n/45. Omega made payments of $1,100 on August 1, $900 on August 10, and $800 on August 31. What amount was still owed on September 1?

Question 50

Given the following: Determine:
a) The amount of mark-up.
b) The amount of operating (overhead) expenses.
c) The operating profit or loss.
d) The rate of mark-up on cost.
e) The rate of mark-up on selling price.

Question 51

On August 6, A&B Construction has three outstanding invoices payable to Excel Builder's Supply. Invoice 535, dated July 16, is for $3,228.56; Invoice 598, dated July 24, is for $2,945.31; and Invoice 678, dated August 3, is for $6217.69. All invoices have terms 4/10, 2/20, n/60. If A&B makes a $10,000 payment to Excel on August 6, what further payment on August 15 will settle the account? Note that Excel applies payments to the oldest invoices first.

Question 52

For a given dollar amount of mark-up, which will be the larger number: the rate of mark-up on cost or the rate of mark-up on selling price? Explain.

Question 53

A payment of $500 on an invoice for $887 reduced the balance owed to $378.09. What cash discount rate was allowed on the $500 payment?

Question 54

Given the following: Determine:
a) The amount of mark-up.
b) The amount of operating (overhead) expenses.
c) The operating profit or loss.
d) The rate of mark-up on cost.
e) The rate of mark-up on selling price.

Question 55

Is it possible for the rate of mark-up on selling price to exceed 100%? Explain.

Question 56

Custom Kitchens received an invoice dated November 17 from Idea Cabinets Ltd. for $7260 with terms 3/15, 1½/30, n/60. If Custom Kitchens made a payment of $4000 on December 2, what further payment on December 16 will settle the account?

Question 57

Pet Mart purchased a litter of six puppies from a reputable breeder for $121 each. If the rate of mark-up on selling price is 45%,
a) What is the selling price of each puppy?
b) What is the rate of mark-up on cost?

Question 58

Given the following: Determine:
a) The amount of mark-up.
b) The amount of operating (overhead) expenses.
c) The operating profit or loss.
d) The rate of mark-up on cost.
e) The rate of mark-up on selling price.

Question 59

The Simcoe School Board has three invoices from Johnston Transport, all with terms 2/10, 1/20, n/60. Invoice 277, dated October 22, is for $14,200; Invoice 327, dated November 2, is for $8,600; and Invoice 341, dated November 3, is for $11,500. What total payment to Johnston on November 12 will settle all three invoices?

Question 60

Peak Roofing sent Jensen Builders an invoice dated July 12 for $5,400 with terms 3/10, 1½/20, n/45. Jensen made a payment of $2,000 on July 20, and a second payment on August 1 that reduced the balance owed to $1,000. What was the size of the second payment?

Question 61

If an item is marked down by the same percentage as the rate of mark-up on selling price, will the reduced operating profit be positive, negative, or zero? Explain.

Question 62

Nelson Hardware ordered a shipment of gas barbecues at a suggested retail price of $459 less trade discounts of 25% and 10%. The manager intends to sell the barbecues at the suggested retail price. If overhead expenses are 20% of the selling price:
a) What will be the unit operating profit?
b) What is the rate of mark-up on cost?
c) What is the rate of mark-up on selling price?
d) What would be the break-even selling price for an inventory clearance sale? (Remember that "break-even" means no profit or loss results from the sale.)

Question 63

Beaver Building Supply obtains 4- by 8-ft sheets of half-inch plywood from Macmillan Forest Products at $34 per sheet less 30% and 5%. The price is to be set to cover Beaver's overhead of 20% of the selling price and to provide an operating profit of 12% of the selling price. What should be the retail price per sheet?

Question 64

The Shoe Shop's normal rate of mark-up on selling price is 45%. What rate of markdown can the store offer on a pair of shoes normally priced at $140, and still realize a 20% rate of mark-up on cost at the sale price?

Question 65

What is the cost of an item that sells for $87.49 if:
a) The rate of mark-up on cost is 30%?
b) The rate of mark-up on selling price is 30%?

Question 66

A pharmacy marks up its springtime shipment of sunglasses to provide for overhead expenses of 40% of cost and a profit of 70% of cost. At the end of the summer, what rate of markdown can the pharmacy apply to the remaining inventory of sunglasses and still break even on sales at this level?

Question 67

Bosley's Pet Foods buys dog kibble for $19.50 per bag less 40%. The store's overhead is 33 % of the selling price, and the desired profit is 10% of the selling price.
a) At what price per bag should the dog food be sold?
b) At this price, what is the rate of mark-up on cost?
c) What is the break-even price?

Question 68

Merchants C and D sell the same article at $69.95 and $64.95, respectively. They both advertise that they will match the price offered by any other store on any product that they stock.
a) What discount rate must C give to match D's price marked down by 20% during a sale?
b) What discount rate must D give to match C's price marked down by 20% during a sale?

Question 69

The rate of mark-up on the cost of a badminton racquet selling at $54.95 is 45%.
a) What was the cost of the raquet to the retailer?
b) What is the rate of mark-up based on selling price?

Question 70

Worker's World bought 250 pairs of rubber boots at $15 per pair. The manager applies a 90% rate of mark-up on cost when pricing footwear. What is the operating profit per pair if overhead expenses work out on average to be 20% of the selling price?

Question 71

Digital Devices plans to stop carrying the Casio FC-200 calculator. It normally marks up the calculator from the $31.50 wholesale cost to the regular selling price of $51.98.
a) What is the normal rate of mark-up on selling price?
b) What rate of markdown can be advertised if Digital Devices wishes to clear out the stock at $31.50, the wholesale cost?

Question 72

In February, Long Lake Nursery ordered lawn fertilizer at $18.60 less 33 ½%, 12 ½%, and 5% per 20-kg bag. The fertilizer is normally priced to provide a 55% rate of mark-up on selling price. Operating (overhead) expenses are 30% of cost. To clear out the remaining bags of fertilizer in July, they were marked down by 45%. Calculate:
a) The net cost per bag.
b) The operating expenses per bag.
c) The regular selling price.
d) The sale price (reduced selling price).
e) The reduced mark-up at the sale price.
f) The operating profit or loss at the sale price.
g) The rate of mark-up on the sale price.

Question 73

A retailer pays $81 to a wholesaler for an article. The retail price is set using a rate of mark-up on selling price of 40%. To increase traffic to his store, the retailer marks the article down 20% during a sale. What is the sale price?

Question 74

Central Ski and Cycle purchased 50 pairs of ski boots for $360 per pair less 33 % and 10%. The regular rate of mark-up on selling price on the boots is 40%. The store's overhead is 22% of the selling price. During a January clearance sale, the price was reduced to $270 per pair.
a) What was the rate of markdown for the sale?
b) What was the profit or loss on each pair of boots at the sale price?
c) At the sale price, what was the rate of mark-up on cost?

Question 75

The Annapolis Rotary Club sells hot dogs for $1.95 each at the annual Annapolis Fall Fair. The Rotary Club buys wieners at $3.95 per package of 10 wieners, and hot dog buns at $2.90 per dozen. It costs $78 for enough condiments for 1,000 hot dogs. What are the Rotary Club's rate of mark-up on selling price and rate of mark-up on cost?

Question 76

Suppose an item that originally had a 40% rate of mark-up on cost is marked down 40%. Is its reduced selling price equal to C? Explain.

Question 77

Morgan's Department Store mailed out 15%-off coupons for its 20^th Anniversary Sale. The coupons may be used for any products in the store. For items already on sale, the coupon applies to the sale price.
a) What price would a coupon-holder pay for a bedspread (regular price $295) already on sale at 20% off?
b) What single rate of markdown would have the same effect as the two price reductions?

Question 78

Just Desserts buys cheesecakes from General Bakeries at $33.60 per cheesecake. It then cuts each cheesecake into 16 slices and sells them to customers at $6.50 per slice. Calculate the rate of mark-up on cost and the rate of mark-up on selling price.

Question 79

Maritime Cellular purchases a BlackBerry smart-phone model for $595 less trade discounts of 20% and 10%.Maritime's overhead expenses are $59 per unit.
a) What should be the selling price to generate a profit of $40 per phone?
b) What is the rate of mark-up on cost?
c) What is the rate of mark-up on selling price?
d) What would be the break-even selling price for a clear-out sale in preparation for the launch of the new model?

Question 80

A florist buys potted poinsettias from a nursery at $15 each less 40% and 10%. The florist prices her stock to allow for overhead of 55% of cost and an operating profit of 20% of the selling price. At what price should she sell the poinsettias?