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ó. At 23 cents a pound, what will 12 firkins of butter cost ?
6. If $ 22 is paid for a barrel of pork, how much is that by the pound?
Ans. 11 cents. 7. How much must be paid for 302 hogsheads of salt at $ 0.30 a bushel ?
Ans. $ 724.80. 8. At $ 4 per quintal, how many pounds of fish may be bought for $50.24?
Ans. 1256 pounds. 9. If the wholesale price of one writing-book be 41 cents, what will be the cost of a great-gross of writing-books ?
10. A dairyman sells 2 firkins of butter at 20 cents a pound, and takės in pay half a barrel of flour at 5 cents a pound, and the balance in cash. How much cash does he receive ?
Ans. $ 17.50.
MISCELLANEOUS EXAMPLES IN REDUCTION.
1. In 57£. 15s. how many half-pence? Ans. 27720. 2. In 59lb. 13pwt. 15gr. how many grains ? 3. In 340167 grains how many pounds ? 4. How many ells English in 761 yards?
Ans. 608 E. E. 4qr. 5. How many yards in 61 ells Flemish ? Ans. 45yd. 3qr.
6. How many bottles, that contain 3 pints each, will it take to hold a hogshead of wine?
Ans. 168. 7. How many steps, of 2ft. 8in. each, will a man take in walking from Bradford to Newburyport, the distance being fifteen miles ?
Ans. 29700. 8. How many spoons, each weighing 2oz. 12pwt., can be made from 5lb. 2oz. 8pwt. of silver?
Ans. 24. 9. How many times will the wheel of a coach revolve, whose circumference is 14ft. 9in., in passing from Boston to Washington, the distance being 436 miles ? Ans. 156073379
10. I have a field of corn, consisting of 123 rows, and each row contains 78 hills, and each hill has 4 ears of corn; now if it takes 8 ears of corn to make a quart, how many bushels does the field contain ?
Ans. 149bu. 3pk. 5qt. Opt. 11. If it take 5yd. 2qr. 3na. to make a suit of clothes, how many suits can be made from 182 yards ? 12. A goldsmith wishes to make a number of rings, each
weighing 5pwt. 10gr., from 3lb. loz. 2pwt. 2gr. of gold; low many will there be ?
Ans. 137. 13. How many shingles will it take to cover the roof of a building, which is 60 feet long and 56 feet wide, allowing each shingle to be 4 inches wide and 18 inches long, and to lie one third to the weather?
Ans. 20160. 14. There is a house 56 feet long, and each of the two sides of the roof is 25 feet wide ; how many shingles will it take to cover it, if it require 6 shingles to cover a square foot ?
Ans. 16800. 15. If a man can travel 22m. 3fur. 17rd. a day, how long would it take him to walk round the globe, the distance being about 25000 miles ?
Ans. 11144144 days. 16. If a family consume 7lb. 10oz. of sugar in a week, how long would 10cwt. 3qr. 161b. last them ? Ans. 1431 weeks.
17. What will 7 hogsheads of wine cost, at 9 cents a quart? 18. What will 15 hogsheads of beer cost, at 3 cents a
Ans. $ 194.40. 19. What will 73 bushels of meal cost, at 2 cents quart?
Ans. $ 46.72. 20. A merchant has 29 bales of cotton cloth ; each bale contains 57 yards ; what is the value of the whole at 15 cents a yard?
Ans. $ 247.95. 21. There is a certain pile of wood 120 feet long, 41 feet high, and 4 feet wide; what is its value at $ 4.00 per cord ?
Ans. $ 67.50. 22. How much must be paid, at twenty cents a square yard, for plastering overhead in a room which is 33 feet long and 18 feet wide ?
23. An apothecary, in compounding 20 boxes of pills, each box containing 25 pills, used 6 grains of aloes, 5 grains of rhubarb, and 4 grains of calomel in each pill. What was the entire quantity used ?
Ans. 7500 grains. 24. Purchased a cargo of molasses, consisting of 87 hogsheads; what is the value of it at 33 cents a gallon ?
Ans. $ 1808.73. 25. If a cubic foot of white-oak wood weighs 880 ounces, and a cubic foot of white-pine wood weighs 480 ounces, how much will a load weigh, which is composed of half a cord of white-oak, and of a cord of white-pine ? Ans. 7360lbs.
26. How many chests of tea, weighing 24 pounds, at 43 cents a pound, can be bought for $ 1548 ?
27. Joseph Eldredge received $ 10, as a birthday present, from his father, on every 29th day of February, from 1837 to 1857. How much less than $ 200 did he receive, in all ?
Ans. $ 150. 28. If 25% grains of standard gold be worth $1, how many pounds avoirdupois of standard gold will be worth $ 1,000,000 ?
Ans. 36854 pounds. 29. A merchant, who had bought 188 gallons of molasses, at 40 cents a gallon, intended to have it sold at the rate of 50 cents a gallon ; but his shop-boy retailed half of the quantity at 124 cents a quart, beer measure, when, finding he had made a blunder, he sold the balance at 14 cents a quart, wine measure, thereby expecting to exactly make up for the mistake. How much less did the whole bring than was intended ?
Ans. $ 2.86.
ADDITION OF COMPOUND NUMBERS.
145. ADDITION of Compound Numbers is the process of finding the amount of two or more compound numbers.
Ex. 1. Required the amount of 31£. 17s. 9d. 2far.; 16£. 16s. 6d. 1far.; 16£. 11s. 11d. 1 far.; 19£. 195. 9d. 3far. ; 61£. 17s. 1d. 2far.
Ans. 147 £. 3s. 2d. 1 far. Having written units of the same
far. denomination in the same column, we 31 17 9 2
find the sum of farthings in the right1 6 16 6 1 hand column to be 9 farthings 2d. 16 11 11 1 1far. We write the 1far. under the 19
19 9 3 column of farthings, and carry the 2d. 61 17 1 2
to the column of pence; the sum of
which is 38d. 3s. 2d. We write Ans. 1 47 3 2 1 the 2d. under the column of pence,
and carry the 3s. to the column of shillings; the sum of which is 83s. 4£. 3s. Having written the 3s. under the column of shillings, we carry the 4£. to the column of pounds, and find the entire amount sought to be 147£. 3s. 2d. 1far.
The same result can be arrived at by reducing the numbers as they are added in their respective columns. Thus, beginning with farthings, we can add, in this way: 2far. + 3far. 5far.
and 1 far. 1d. 2far., and 1far. 1d. 3far., and 2far. 2d. 1 far. Writing the 1 far. under the column of farthings, we carry the 2d. to the column of pence; and add, 2d. (carried) + 1 3d., and 9d. 12d.
· 1s., and 11d. 1s. 11d., and 6d. - 2s. 5d., and 9d. 3s. 2d. Writing the 2d. under the column of pence, we carry the 3s. to the column of shillings; and add, 3s. (carried) + 17s. 20s. =1£., and 19s. 1£. 198., and 11s. 2£. 10s., and 16s. : 3£. 6s., and 17s. 4£. 3s. Writing the 3s. under the column of shillings, we carry the 4£. to the column of pounds, and so find the whole amount to be, as before, 147£. 3s. 2d. ifar.
The last method of operation may be rendered more concise, as it should always be in practice, by merely naming results as the adding is performed (Art. 45).
From the illustrations given, it is evident that the adding of compound numbers is like that of simple numbers, except in carrying ; which difference holds also in subtracting, multiplying, and dividing compound numbers.
RULE. - Write all the given numbers, so that units of the same denomination may stand in the same column.
Add as in addition of simple numbers; and carry, from column to column, one for as many units as it takes of the denomination added to make a unit of the denomination next higher.
Proof. The proof is the same as in addition of simple numbers.
NOTE. - As half a mile is equal to 4 furlongs, we add them to the 1 furlong, which makes 5 furlongs. And as half a foot is equal to 6 inches, we add them to the 7 inches, which makes 13 inches; and these are equal to 1 foot 1 inch.
10. Add together 37yd. 3qr. 3na. 2in.; 61yd. 3qr. Ina. lin.; 13yd. 2qr. 2na. 2in. ; 32yd. lqr. Ina. lin.; 61yd. 2qr. 2na. 2in.; and 22yd. lqr. 3na. Ans. 229yd. 3qr. 3na. 1 fin.
11. Add together 671E.E. Iqr. Ina. lin.; 161 E.E. 3qr. 3na. 2in.; 617E.E. 3qr. Ina. 2in.; 178E.E. 3qr. 2na. lin.; 717E.E. 2qr. Ina. 2in.; and 166 EE. 3qr. 2na. lin.
12. Add together 761A. 3R. 37p. 260ft. 125in. ; 131A. 2R. 16p. 135ft. 112in. ; 613A. IR. 14p. 116ft. 131in.; 161 A. 3R. 13p. 116ft. 123in. ; 321 A. 2R. 31p. 97ft. 96in.; and 47 A. 3R. 19p. 91ft. 48in.
Ans. 2038A. 1R. 13p. 2ft. 95in. 13. Add together 38A. 1R. 39p. 272ft. ; 61A, 3R. 38p. 167ft. ; 35 A. 3R. 19p. 198ft. ; 47A. 3R. 16p. 271ft.; 86A. 2R. 13p. 198ft. ; and 46A. 1R. 14p. 269ft. 14. Add together 17m. 7fur. 9ch. 3p. 241. ; 16m. 3fur. 4ch.