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59. Practical and Miscellaneous Problems.
1. If 8 acres of land cost £137 14s. 6d. 1 far., how much will 1 acre cost?
2. If 7 equal casks of wine contain 459 gal. 1 qt. 1 pt. 3 gi., how much does each cask contain ?
3. I divided 10 A. 1 R. 13 sq. rd. 25 sq. yd. 7 sq. ft. 125 sq. in. of land into 11 equal lots, how much will each lot contain ?
4. A railroad 43 m. 5 fur. 23 rd. long, was divided into 4 equal sections. How long was each section?
5. 11 equal bars of silver weighed 31 lb. 5 oz. 16 dwt. 15 gr. What was the weight of each bar?
6. When 8 cwt. 2 qr. 20 lb. 14 oz. of iron can be bought for $9, how much can be bought for $1 ?
7. If 8 barrels of apples contain 22 bu. 3 pk., how much does 1 barrel contain ?
8. A corn dealer bought 47 bu. 3 pk. 5 qt. of corn at one time, 85 bu. 2 pk. 6 gt. at another, and 65 bu. 1 pk. 7 qt. at another. He sold it in 4 equal lots. How much was there in each lot?
9. A man bought 7 stacks of hay, each containing 5 T. 17 cwt. 3 qr. 19 lb. He carried the hay to market in 21 equal loads. What was the weight of each load ?
10. An apothecary mixed together lib 53 73 27 15 gr. of one drug; 21b 113 53 17 18 gr. of another; lib 53 of another; and 73 53 19 17 gr. of another. He then divided the whole into 20 equal portions. What was the weight of each portion ?
11. A goldsmith who had 19 oz. 13 dwt. 15 gr. of gold dust, bought 5 lots, each weighing 13 oz. 9 dwt. 17 gr. He afterwards sold 1 lb. 3 oz. 5 gr. of it, and made the rest into 3 equal bars. What was the weight of each bar ?
12. I gave 37 yards of cloth, at $4 per yard, for apples at $3 per barrel. How many barrels of apples did I obtain ?
13. A man's annual income was $1500. His house rent was $275 per year; his family expenses were 3 times as much as his house rent, lacking $42.70; and his travelling and miscellaneous expenses were $83.25 less than $ of his family expenses. How much could he save per year?
14. A drover bought 27 head of cattle, at $38.25 per head. It cost him $25.38 to drive them to market, and he sold them at $42.35 per head. What did he gain on them?
15. I bought 17 cases of shoes, each case containing 50 pairs, at $1.97 per pair. It cost me 75 cents per case to have them carried to my store, and I sold them for $2.31 per pair. What did I gain on them?
16. If a man's income is $365 per year, and he spends $289.75 per year, how much will he save in 9 years ?
17. I bought 127 acres of land at $19.50 per acre, and sold it at $27.25 per acre. How much did I gain ?
18. A mechanic finds that on the average he earns $1.875 per day, and works 22 days per month. Now if his necessary expenses are $28.25 per month, how many years and months will it take him to lay up $1000?
19. A man who had $2625 bought 123 barrels of four at $7 per barrel, and invested the rest of his money in flour at $6 per barrel. How many barrels were there in the last lot?
20. If 9 pieces of cloth cost £15 178. 10d. 3 far. per piece, and sell for £19 48. 3d. per piece, what is the gain ?
21. How many horse-shoes each weighing 12 oz. 5 dr. can be made from 9 bars of iron each weighing 19 lb. 8 oz. ? (See note following the 61st problem in 53.)
22. How many steps must a boy take in going to and returning from school, provided that he lives 2345 yards from the schoolhouse, and that his steps are 2 ft. 6 in. in length ?
23. An Englishman gave £148 178. 6d. for tea at 28. 6d. per pound, and sold it for 38. per pound. What did he gain on it?
24. A farmer bought 37 lb. of sugar at $.09 per pound ; 14 lb. of coffee at $.17 per pound; 3 lb. of tea at $.45 per pound; 3 yd. of cloth at $2.63 per yard ; a hat for $3.75; and a coat for $9.37; giving in payment 29 lb. of butter at $.19 per pound, and the rest in money. How much money did he pay?
25. How much will a pile of wood 84 ft. long, 8 ft. high, and 4 ft. wide, cost at $3.67 per cord ?
26. How much will a lot of land, 80 rods long and 72 rods wide, cost at $87.30 per acre ?
27. My garden is 229 ft. long and 137 ft. wide. Within the garden, but next to the outer edge, and extending completely around it, I have made a gravel-walk 3 ft. wide. How many square feet does the walk contain ?
Note.- In solving such problems as the above, the pupil should draw a figure or plan of the surface to be measured.
28. A man who owns a garden 128 ft. long and 116 ft. wide, lays out a flower-bed 2 ft. wide, next the outer edge, and extending completely around it. How many square feet does the bed contain ?
29. How many square feet are there in the four walls of a room 16 ft. long, 14 ft. wide, and 9 ft. high?
30. How many square feet are there in the top and walls of a ball 37 ft. long, 34 ft. wide, and 13 ft. high?
31. My orchard is 24 rods long and contains 3 acres. How wide is it? How much will it cost to build a fence round it at $1.75 per rod ?
32. George has $157, William has $19 more than twice as much as George, Joseph has $69 more than George and William together, and Robert has $25 less than as much as Joseph. How many dollars has each of the boys ?
33. A man who had 325 gal. 2 qt. 1 pt. of wine, sold 239 gal. 3 qt. 1 pt. at 25 cents per pint, and put the rest into bottles, each holding 1 pt. 3 gi. How many pints did he sell? How much did he receive for what he sold ? How many bottles did he fill?
CONTRACTIONS AND ABBREVIATED
60. To multiply by two or more Figures at one Operation.
(a.) We may multiply by two or more figures at one operation, by observing that the lowest denomination of the product will be found by multiplying the lowest denomination of the multiplicand by the lowest denomination of the multiplier; that the next denomination of the product will be found by multiplying the second of the multiplicand by the first of the multiplier, and the first of the multiplicand by the second of the multiplier, etc.
1. What is the product of 2476 x 48 ?
PRELIMINARY EXPLANATION. — We shall obtain the units of the product by multiplying 6 units by 8 units. We shall obtain the tens of the product by multiplying 7 tens by 8 units, and 6 units by 4 tens. We shall obtain
tens by 4 tens. We shall obtain the other denominations in a similar manner. Hence the following solution.
SOLýtion. - 8 times 6 units are 48 units. 8 times 7 teng 48
are 56 tens, and 4 tens (from the last product) are 60 tens,
and 4 tens times 6 units or 24 tens are 84 tens; 8 times 4 118848
hundreds are 32 hundreds, and 8 hundreds (from the last product) are 40 hundreds, and 4 tens times 7 tens or 28 hundreds are 68 hundreds. 8 times 2 thousands, etc.
61. To multiply by 99, 999, etc.
(a.) Since 99 = 100 – 1, 999 = 1000 - 1, etc. it follows that 99 times a number must equal 100 times the number, minus the number. 999 times a number must equal 1000 times the number, minus the number. 98 times a number must equal 100 times the number, minus twice the number, etc.
62. To Multiply by any convenient Fractional Part of 100,
(a.) It is obvious that the product of a number multiplied by 1, 4, or of 10, must be , }, or 1 of 10 times the number. The product of a number multiplied by t, ß, or 4 of 100, must be , t, or 1 of 100 times the number; and so of any fractional part of 10, 100, 1000, 10000, etc.
1. What is the product of 9473 x 166%?
SOLUTION. — Since 166 = of 1000, the required product must equal of 1000 times 9473, or £ of 9473000, which is 1578833. (b.) Find the following products : 2. 6438 x 121.
6. 4839 X 331. 3. 8651 x 25.
6. 5479 x 16. 4. 7327 x 125.
7. 8625 X 1lf.