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136 Divide .007 by .5.
1. If 1.4 cwt of sugar cost $10.09, what will 9 cwt. 3
grs. cost ?
2. If 193 yards of cloth cost $128.35, what will 18 yds. 3
grs. cost ?
3. If 23} yds. of riband cost $54, what will 344 yds. cost ?
4. If 3 cwt. 2 qrs. 14 lb. of sugar cost $38.55 what will 19 cwt. 1 qr. 17 lb. cost ?
5. If į cwt. of tobacco cost 4£. 18s., how much may be bought for 13£. 17s. 8d. ?
6. Sold 75 chaldrons of lime, at 11s. 6d. per chaldron ; how much did it come to ?
7. A goldsmith sold a tankard for 10£. 13s., at the rate of 5s. 6d. per oz.; hɔw much did it weigh?
8. Goliah the Philistine is said to have been 61 cubits high, each cubit being 1 ft. 7.168 English inches ; what was bis height in English feet?
9. "How many yards of flannel that is 1 English ell wide will be sufficient to line a cloak containing 8; yds., that is yd. wide ?
10. I agreed for a carriage of 2.5 tons of goods 2.9 miles, for 75 of a guinea ; what is that per cwt. for 1 mile ?
11. If a traveller perform a journey in 35.3 days, when the days are 11.374 hours long; in how many days will he perform it, when the days are 9.13 hours long?
12. If 12 men can do 125 rods of ditching in 653 days; in how many days can they do 242, rods?
13. In a room 18 ft. 6 in. long, and 14 ft. 9 in. wide, how many square feet? In a yard of carpeting that is 2 ft. 8 in. wide, how many square feet? How many yards of such carpeting will cover the above mentioned floor?
14. How many yards of carpeting that is 14 yd. wide will cover a floor 22 ft. 7 in. long, and 19 ft. 8 in. wide ?
15. How many feet of boards will it take to cover the walls of a house 32 ft. 8 in. long, 26 ft. 4 in. wide, and 26 ft. 5 in. high? How much will they cost at $3.50 per 1000 feet ?
16. How many feet will it take to cover the floors of the above house?
17. If 1000, or a bunch, of shingles will cover 10 feet square, how many bunches will it take to cover the roof of the above house, allowing the length of the rafters to be 16 ft. 5 in. ?
18. In a piece of land 37; rods long, and 32g rods wide, how many acres ?
19. What will a piece of land, measuring 57 ft. in length, and 43 st. in breadth, come to, at the rate of $25 per square rod ?
20. In a pile of wood 23 st. 7 in. long, 3 ft. 10 in. wide, and 4 ft. 3 in. high, how many cords ?
21. How many feet of wood in a load 8 ft. long, 4 ft. wide, and 3 ft. 8 in. high ?
N. B. Wood prepared for the market is generally 4 feet long, and a load in a wagon generally contains two lengths, or 8 feet in length. If a load is 4 feet high and 4 feet wide, it contains a cord. It was remarked above, that what is called one foot of wood, is 16 solid feet, and that 8 such feet make 1 cord. To find how many of these feet a pile or load of wood contains, it is necessary to find the number of solid feet in it, and then to divide by 16. When the load of wood is 8 feet long, we may multiply the breadth and height together, and then, instead of multiplying by 8, and dividing by 16, we may divide at first by 2, and the same result will be obtained.
22. How many feet of wood in a load 8 feet long, 3 ft. 4 in. wide, and 2 ft. 7 in. high ?
23. How many feet of wood in a load 8 feet long, 3 ft. in. wide, and 5 ft. 2 in. high ?
24. How much wood in a load 8 ft. long, 4 ft. 2 in, wide, and 5 ft. 4 in. high ?
25. If a load of wood is 8 ft. long, and 3 st. 7 in. wide, how high must it be to make a cord?
26. How many bricks 8 inches long, 4 inches wide, and
21 inches thick, will it take to build a house 44 feet long, 40 feet wide, 20 feet high, and the walls 12 inches thick ?
27. What is the value of 87 pigs of lead, each weighing 3 cwt. 2 qrs. 173 lb., at 8£. 13s. 8d. per fother of 194 cwt. ?
28. What is the tax upon $1153, at $.03 on a dollar ? 29. What is the tax upon $843.35, at $.04 on a dollar ?
30. What is the tax upon 785£. 11s. 4d. at 2s. 5d. on the pound?
31. Suppose a certain town is to pay a tax of $6145.88, and the whole property of the town is valued at $153647'; what is that on a dollar ? How inuch must a man pay, whose property is valued at $23475.67 ?
Note. In assessing taxes, the first requisite is to have an inventory of the property, both real and personal, of the whole town or parish, and also of each individual who is to be taxed, and the number of polls. The polls are always stated at a certain rate. Then knowing the whole tax, take out what the polls amount to, and the remainder is to be laid upon the property. Find how much each dollar is to pay, and make a table, containing the portion for 1, 2, 3, &c. to 10 dollars, then for 20, 30, 40, &c. to 100, and then for 200, 300, &c. From this table it will be easy to find the tax upon the property of any individual.
32. A certain town is taxed $3137.43. The whole property of the town is valued at $89640.76. There are 120 polls which are taxed $.75 each. What is the tax on a dollar ? How much is a man's tax who pays for 3 polls, and whose property is valued at $2507 ?
33. A merchant bought wine for $1.75 per gallon, and sold it for $2.25 per gallon. What per cent. did he gain ?
Note. He gained 50 cents on a gallon, which is 1ts=18 of the first cost. It has been already remarked that 1 per cent. is .01, 2 per cent. is .02, &c.; that is, the rate per cent. is always a decimal fraction carried to two places or hundredths. To find the rate per cent. then, first make a common frac tion, and then change it to a decimal =.285. Now .28 is 28 per cent. and .0055 isi per cent. The rate then 28.520 per cent.
The two first decimal places taken together being hundredths are so much per cent., and thousandths are so many tenths of one per cent.
34. A merchant bought a hhd. of molasses for $20, and sold it for $25; what per cent did he gain ?
35. A merchant bought a quantity of flour for $137, and sold it for $143 ; what per cent. did he gain ?
36. A man bought a quantity of goods for $94.37, and sold them for $83.92. What did he lose per cent. ?
37. A merchant bought molasses for 1s. 8d. per gallon, and sold it for 2s. 3d. per gallon. What did he gain per cent !
38. A merchant bought wine for Ils. 3d. per gallon, and sold it for 9s. 8 d. What per cent. did he lose ?
39. A merchant bought a quantity of goods for 37. 15s 8d.; and sold them again for 43£. 11s. 4d. What per cent did he gain ?
40. A man buys a quantity of goods for $843; what per cent. profit must he make in order to gain $157 ?
41. A man failing in trade owes $19137.43, and his property is valued at $ 13472.19. What per cent. can he
pay 42. A man purchased a quantity of goods, the price of which was $57, but a discount being made, he paid $45.60. What per cent. was the discount ?
43. A man hired $87 for 1 year, and then paid for principal and interest $92.22. What was the rate of the interest ?
44. A man paid $12.81 interest for $183, for 2 years. What was the rate per year !
45. A man paid $13.125 interest for $135, for 1 year and 6 months. What was the rate per year ?
46. A man paid $4.37 interest for $58, for 1 year and 8 months. What was the rate per year ?
47. 4s. 6d. sterling of England is equal to 1 dollar in the United States. What is the value of 1£. sterling in Federal
48. How many dollars in 35£. sterling ? 49. How many dollars in 27£. 14s. 8d. ?
Note. Change the shillings and pence to the decimal of a pound, by the short method shown above. 50. How many dollars in 187£. 17s. 4d. ? 51. In $19.42 how many pounds sterling ? 52. In $157 how many pounds ? 53. In $2334.72 how many pounds ? 54. Bought goods in England to the amount of 123£. 175. 9d. ; expenses for getting on board 3£. 5s. 8d. ; $8.50 freight; duties in Boston 15 per cent on the invoice ; other expenses in Boston $15.75.
How many dollars did the goods cost? How much must they be sold for to gain 12 per cent. on the cost ?
55. What is the interest of 847,50 for 1 year, 7 months, and 13 days, at 7 per cent. ?
Ans. 5.3865 I first find the interest for 1 year, ana then į of that is the interest for 6 months ; ã of the interest for 6 months will be the interest for 1 month ; į of the interest for 1 month will be the interest for 10 days, and of the interest for 10 days is very near the interest for 3 days. All these added together will give the interest for the whole time. In a similar manner, the interest for any time at any rate per cent. may be calculated.
When there are months and days, it is better to calculate the interest first at 6 or 12 per cent., and then change it to the rate required. Observe that 1 per cent. is of 6 per cent., 1} per cent. is į of 6 per cent., 2 per cent is į of 6 per cent, &c. Hence if the rate is 7 per cent., calculate first at 6 per cent., and then add į of it to itself, or if 5 per cent., subtract; if 71 or 4į per cent. add or subtract , &c.
Let us take the above example.
6 per cent. for 1 year, 7 months, and 13 days, is 91o per cent. nearly, that is .097.
$5.3754 This answer agrees with the other within about 1 ceni. Greater accuracy might be attained, by carrying the rate to one or two more decimal places.