915. 7. An ounce avoirdupois contains 7000 gr. ÷ 16; an ounce troy contains 480 gr.

8. 4 lb. 8 oz. avoirdupois = 7000 troy grains × 44.

9. The pure silver amounts to 192.9 gr. x.9; divide by 480 to reduce to ounces, and multiply 75 by the quotient. 75 x 192.9 x .9

NOTE.

[(16+14 +16 +14) × 8]+

- When the bottom of a tank is covered with sheet lead, the side strips will be in. less than 8 ft. high, etc., but this small difference may be neglected in these four problems.

12. Multiply the number of square feet by, and divide the product by 12. Cancel.

21. Assessed value, of $24000, or $18000. Taxes = 1% of $18000.

917. 8. Dividend 24% of ($50 × 65).

=

918. 1. Area of surface to be papered: [(16+14 +16 +14) × 10] - 174; divided by area of roll, 24 ft. by 14 ft.

4. When he sells 31 gills, the grocer charges for 32 gills, or 1 times the correct quantity, thereby charging for more than he gives. In 2 hhd. of 58 gal. 1 qt. 1 pt. each, there are 117 gal., the dishonest gain on which is of 1174 gal. worth $.80 × 31 of 1174.

6. 30% of cost (x) = 21.

63

919. 1. (a) $48.50 + ($48.50 X 180 × 830) = $ 48.50 + .51 = $49.01. Ans.

60

Omitting days of grace, $48.50 + ($48.50 × 180 × 36%) $48.50+.48 $48.984, say $48.99. Ans.

These examples should be worked with days of grace or without days of grace, but not in both ways. See Art. 901. Days of grace were not abolished in New York until January 1895.

(b) With days of grace, this note is due Dec. 17. Term Dec. 1 to Dec. 17 16 days. Discount on $49.01 for 16 days at 6% =$49.01×80%=13. Proceeds $49.01.13 = $48.88

Ans.

=

Omitting days of grace, the note is due Dec. 14. Term = 13 days. Discount on $48.99 for 13 days at 6% = $48.99 × 180 x=11. Proceeds $48.99.11 $48.88. Ans.

13

360

2. With days of grace, the amount due at maturity will be $175+ ($175 × 180 × 398) = $175+2.71+=$177.71+. The term of discount = 93 days - 33 days 60 days. Interest of $177.71 for 60 days at 6% will be $1.78 nearly. Proceeds $177.71 1.78 $175.93. More accurately, $177.7125 1.7771 $175.9354 or $175.94-.

Without days of grace, the amount due at maturity will be $175+ ($175 × 180 × 39%) = $177.63 — .

Interest of this

=

amount for 57 days $1.69. Proceeds $177.63 -1.69

= $175.94.

=

14. Amount furnished, $12000. or, is entitled to of $1800; the second to

The one furnishing $3000, of $1800, etc. 1200 men for 30 and will last 1200

15. After 10 days, there are rations for days; which will last 1 man 30 days × 1200;

men +300 men, (30 days × 1200) ÷ 1500 = Ans.

16. Train leaving B goes 14 times as fast as the other, so that meeting place will be 1 times as far from B as it is from A. If x represents distance from A, 1x will represent distance from B, and x + 1x = 120, or x = 48. Trains meet 48 mi. from A, or 72 mi. from B. The first train takes 18 hr. to travel the distance, or 2 hr. 24 min.; second train requires the same time,

1 hr., or 2 hr. 24 min. Time of meeting = 9 A.M. +2 hr. 24 min. = 24 min. past 11.

=

=

distance trav

Or, let x= time required to reach meeting point; then 20 x distance travelled by one train, and 30 x elled by the other, and 20 x + 30 x

x = 23. Time is 23 hr., etc.

17. x+3x+6x+10x900.

= whole distance =

120, or

18. Let x= share of third; x+75 = share of second; and x+75+48= share of first.

x+x+75+ x + 75 +48 = 540.

19. If 4 men need 105 hr., one man would need 420 hr., and 6 men would need 70 hr., or (70 ÷ 10) da.

х

=

20. Let x = number of dozen bought, 15 x = cost in cents; 14= number of dozen sold, 16 times (x − 1) = 16 x − 20

selling price; 16 x

dozen, or 240 eggs.

20=15x, or x = 20.

-

He bought 20

21. The interest on $250 for 8 mo. is the same as that on $1 for 8 mo. x 250, and on $400 for (8 mo. × 250) ÷ 400, or 5 mo.

22. Provisions for 3000 men would last 1 4000 men, or 18 wk. × 13 = 24 wk. Ans.

times as long as for

24. Area of first plank in square feet, 20×1; of second, 24 xx. 24 x = 20.

x= Ans. in feet, or (× 12) in.

25. He can pay 2025 of his debts. Mr. Smith should receive $576 x 2025. Cancel.

922. 6. See table, Arithmetic, Art. 795.

923. 10. 23 × 11 × x = 2749.

13. 48 × 72 × x = 2150.4 × 40.

2150.4 × 40

x=

Ans. in inches.

48 × 72

22. 55 cts. × 6 × 54 × 32.

924. 1. The pupils should gradually become accustomed to business methods of obtaining results. In calculating

$583.40 29.17

the amount to be paid, a clerk writes the discount at once under the gross price. He takes by dividing by 2 and placing the first quotient figure one place to $554.23 the left.

2. In the first example, a discount of 5% is made for prompt payment; the discount here allowed is a reduction from what is called the "list" price. Catalogues are issued by some merchants on which the prices named are not the ones regularly charged, but are much larger so as to mislead persons that do not know the rate of discount allowed. Information as to this rate is communicated to customers, and varies from time to time owing to fluctuations in the market, the "list" price seldom being changed. The list price is sometimes called the "gross" price, the "net price being the one actually paid.

A bill for the Roman candles would be made out as follows:

16 gross Roman Candles, $26.75, $428.

The product by .60 is written under the "gross" total, the first figure being written two places to the left.

The net cost can be directly obtained by multiplying $428 by .40.

7. Two, three, and even more discounts are very frequent in business. An article catalogued at $100 is sold, for instance, at $70, and customers informed that the discount is 30%. A later reduction in price is accompanied by a notice that a further discount of 10% will be allowed. This does not signify 30% +10%, or 40%, from the "list" price; it means that the regular price of $70 is to be reduced $7, making the new price $63. A third discount of 5% means 5% of the last price, $63; etc., etc. In writing these discounts, the per cent mark is written only after the last.

net" amount of

11. On a bill of $100, 40 and 10% gives a "net $60-$6, or $54; 30 and 20% gives $70-$14, or $56; the former being better for the buyer by $2.

12. $100 less 33 and 10% = $60. The discount is $40 on $100, or 40%. The net is 60%.

13. 100-4060; 20% of 60 = 12; discount=40%+12% = 52%. Ans.

15. The first reduction is 100% - 20%, or 80% of the list; the second is 100% - 10%, or 90% of the former. 90% of 80% =% of 80% = 72%. Ans.

16. 80% of 90% = 72%. Ans. The net price is the same for the same discounts in whatever order they are taken.

925. 3. of 5000 (cents) = 5 (cents); 50x=5; etc.

100

11. Value at par, $50 × 96

=

- $4476 $324=x% of $4800, i.e., 32448x; etc.

15. $500 × 180 × 88.

926. 3. 50% +[10% of (100% - 50%)] = 50% + 5% = 55%. Ans.

4. 30% +[30% of (100% - 30%)]= 30% +(30% of 70%) = 30% +21% = 51%. Ans.

5. of gross price (x) = 729; x=81; x=810.

927. 21. Cost per acre = $40293 ÷ 396, at which price 112

acres were sold.

25. 40×3ק. Cancel.

26. Number of hours 365÷4188.

=