34. The discount on some goods listed at $460 is $115. What is the rate of discount?

35. The discount at 8% on some goods is $41.60. What is the list price?

36. The discount at 121% on some goods is $2.05. What is the list price?

37. A bicycle was marked $45, but was sold at 12% discount. What was the net price?

38. A piano was listed at $550, but was sold at 30% discount. What was the selling price?

39. A jobber bought some goods listed at $2450. He was allowed a discount of 22%. What was the net price?

40. A merchant bought 850 yards of muslin at 6 a yard, less 18%. How much did it all cost?

41. A merchant bought 975 yards of lawn for $146.25, less 20%. How much did he pay per yard?

42. A grocer bought 36 doz. cans of soup listed at $1.75 a dozen. He was allowed a discount of 25%. What was the net price?

43. A dealer sold some boxes of soap, 60 cakes to the box, for $2.25 a box. He was allowed a discount of 20%. How much did he receive per cake?

44. A grocer bought 160 bags of flour, 121 lb. to the bag, listed at 4 a pound. He was allowed a discount of 15%. What did the flour cost him?

45. A grocer bought 24 doz. pound packages of macaroni for $31.20, less 15%. He sold it for 159 per package. How much did he gain in all?

46. After the holidays a man bought some silver goods that had been marked $280 but were now subject to a discount of 12%. How much did they cost him?

14. Discount Series. The changes in cost of production from time to time, and the variation due to the credit of the buyer, and the quantity of goods purchased, give rise frequently to several discounts known as a discount series.

Goods that are selling at a discount of 20% may be produced at a lower cost owing, for example, to an unusually large cotton crop. An additional discount of 10% may then be allowed. Likewise a person whose credit is exceptional, who buys an especially large quantity, or who pays cash, may be entitled to a still further discount of 5%.

In a discount series the first denotes the discount from the list price, the second denotes the discount from the remainder, and so on.

Thus $100 less 20%, 10%, and 5%, means that 20% is taken from $100, leaving $80; then 10% from $80, leaving $72; then 5% from $72, leaving $68.40. The order is, however, immaterial.

When there is a fraction of a cent in a remainder, the seller usually counts it a whole cent in his favor.

The regular discount is quoted first, and then the special discounts. Advantages of a discount series are that it saves reprinting elaborate catalogues, allows of easy change, enables the dealer easily to offer different discounts to different customers, and allows for several options to purchasers.

If a bill is due at once it usually bears the words "Terms cash." If due in 60 days without discount, it may bear the marks "N/60" or "Net 60 da." If due in 60 days, but with a special discount of 3% if paid in 10 days, it may read "3/10, N/60," or "3% 10 da., net 60 da."'

EXERCISE 10

Given these list prices and discounts, find the net prices:

1. $225, 20% and 6%.
2. $368, 25% and 5%.

3. $480, 121% and 3%.
4. $350, 15% and 4%.
5. $560, 25% and 10%.
6. $270, 331% and 10%.

7. $480, 25%, 10%, 5%. 8. $560, 25%, 20%, 3%. 9. $729, 331%, 10%, 10%. 10. $280, 25%, 10%, 10%. 11. $2760, 331%, 20%, 10%. 12. $5550, 331%, 25%, 15%.

13. How much will 240 ft. of iron pipe cost if listed at $1.50 a foot, a discount of 40% and 10% being allowed?

14. How much will a gross of jars of mixed pickles cost at $6 a dozen, a discount of 20% and 10% being allowed?

15. The list price of 2-pound cartons of prunes is $24 per 100. A discount of 20% and 10% is allowed. What is the net price of 300 cartons?

16. A book dealer can buy an encyclopedia for $60 less 20% and 10%, or for the same price less 15% and 15%. Which is the better for him, and how much better?

17. A grocer buys 100 dozen jars of table salt listed at $1.50 a dozen, a discount of 25% and 8% being allowed. If he sells the salt at 12 a jar, how much does he gain?

18. A dry goods dealer buys 960 yd. of silk listed at $1.50 a yard, a discount of 33% and 5% being allowed. If he sells it at $1.50 a yard, how much does he gain?

19. A dealer buys 36 doz. pocket knives listed at $8.40 a dozen, a discount of 25% and 10% being allowed. If he sells them at 75g apiece, how much does he gain ?

20. A furniture dealer buys 16 bedroom sets listed at $36 each, a discount of 163% and 10% being allowed. If he sells the furniture at $36 a set, how much does he gain?

21. A hardware dealer bought a shipment of stoves. After deducting a discount of 33% and 25%, and paying $9.75 freight and $2.50 cartage, the stoves cost him $252.25. What was the list price of the stoves?

22. A dry goods dealer bought a shipment of cloth. After deducting a discount of 25% and 10%, and paying $8.50 for freight and cartage, the cloth cost him $410. What was the list price?

15. Bills Discounted. The following is a common form of a bill of goods purchased from a wholesale dealer.

Chicago, March 15, 19.........

Mr. R. D. Seanlan, Springfield, Ill.

Bought of Lane & Company, Jewelers 1072 Wabash Avenue

Terms 20%, 10%

Feb. 10. 8 doz. apoone No. 487 @ $14.75
7 doz. plated forks No.511 @ $4.20

$118.00

29.40

$147.40

Make out bills for the following:

1. 36 doz. files at $6.25; 3 doz. saws at $17.50. Discounts 30%, 20%.

2. 960 yd. silk at $1.40; 840 yd. velvet at $1.60. Discounts 25%, 10%.

3. 4 doz. pr. hinges at $4.60; 25 doz. table knives at $8.40. Discounts 20%, 10%.

4. 12 doz. locks at $4.20; 6 doz. mortise locks at $4.60. Discounts 25%, 8%.

5. 360 yd. taffeta at 987; 4 gross pompons at $144; 3 doz. pieces braid at $20.40. Discounts 10%, 5%.

6. 60 lb. brads at 6; 200 bolts at $4.80 per C; 6 doz. knives at $7.20. Discounts 40%, 20%, 10%.

7. 480 yd. silk at $1.60; 640 yd. lawn at 22; 960 yd. taffeta at 969. Discounts 10%, 5%, 5%.

16. Single Discount equal to a Series. It is often convenient to find a single discount equal to a series.

For example, find the single discount equal to the discount series 20%, 10%, and 10%.

Let the list price be represented by 100 % of the list price.

Then deducting 20% of this, or

we have

Deducting 10% of this, or

we have

Deducting 10% of this, or

we have

20% of the list price,

80% of the list price.
8 % of the list price,

72 % of the list price.

7.2% of the list price, 64.8% of the list price.

Then 100%-64.8% = 35.2%, the single discount.

EXERCISE 12

Find the single discount equal to the discount series:

17. Compare the single discount equal to the series 10% and 5%, with the sum of 10% and 5% minus the product of 10% and 5%.

18. By the method suggested in Ex. 17, find the single discount equal to the series 20%, 5%.

19. How does the single discount equal to the discount series 20%, 10%, and 5%, compare with that equal to the discount series 10%, 5%, and 20%? Prove it.