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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. 3685 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 12 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. 1far.; 19£. 19s. 9d. 3far.; 61£. 17s. 1d. 2far. Ans. 147£. 3s. 2d. 1far.

OPERATION.

8.

£.
d. far.
31 17 9 2
16 16 6 1
16 11 11 1

19

61

19 9 3
17 1 2

=

Having written units of the same denomination in the same column, we find the sum of farthings in the righthand column to be 9 farthings = 2d. 1far. We write the 1far. under the column of farthings, and carry the 2d. to the column of pence; the sum of which is 38d. : 3s. 2d. We write 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. 1d. 1far.;

Ans. 147 3 2 1

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and 1far.

=

1d. 3far., and 2far.

1d. 2far., and 1far. = 2d. 1far. Writing the 1far. under the column of farthings, we carry the 2d. to the column of pence; and add, 2d. (carried) +1

12d.

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3d., and 9d.
= 3s.

=

1s., and 11d. 1s. 11d., and 6d. : 2s. 5d., and 9d. 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. 19s., and 11s. = 2. 10s., and 16s. 3£. 6s., and 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.

17s. 4£. 3s.

=

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. numbers.

The proof is the same as in addition of simple

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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. 1na. lin.; 13yd. 2qr. 2na. 2in.; 32yd. 1qr. 1na. lin.; 61yd. 2qr. 2na. 2in.; and 22yd. 1qr. 3na. Ans. 229yd. 3qr. 3na. 1țin.

11. Add together 671E.E. 1qr. 1na. lin.; 161E.E. 3qr. 3na. 2in.; 617E.E. 3qr. 1na. 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. 1R. 14p. 116ft. 131in.; 161A. 3R. 13p. 116ft. 123in.; 321A. 2R. 31p. 97ft. 96in.; and 47A. 3R. 19p. 91ft. 48in. Ans. 2038A. 1R. 13p. 2ft. 95in. 13. Add together 38A. 1R. 39p. 272ft.; 61A. 3R. 38p. 167ft.; 35A. 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.

1p. 151.; 27m. 4fur. 6ch. 2p. 171.; 18m. 6fur. 3ch. 3p. 211.; 61m. 7fur. 7ch. 2p. 161.; and 17m. 1fur. 8ch. 2p. 191.

Ans. 160m. Ofur. 1ch. 1p. 121.

15. Required the sum of 27m. 4fur. 3ch. 1p. 211.; 29m. 3fur. 1ch. 3p. 231.; 67m. 3fur. 3ch. 1p. 191.; 21m. 7fur. 1ch. 3p. 161.; 16m. 7fur. 9ch. 3p. 131.; and 31m. 4fur. 8ch. 1p. 201.

16. Required the value of 29T. 36ft. 1279in. 69T. 19ft. 1345in. + 67T. 18ft. 1099in. + 71T. 14ft. 1727in. + 43T. 35ft. 916in. 53T. 17ft. 1719in.

Ans. 335T. 23ft. 1173in. 17. Add together 61C. 127ft. 1161in.; 37C. 89ft. 1711in.; 61C. 98ft. 1336in.; 43C. 56ft. 1678in. 91°C. 119ft. 1357in. and 81C. 115ft. 1129in.

18. Required the value of 61 tuns 3hhd. 62gal. 3qt. 1pt. + 39 tuns 2hhd. 16gal. 1qt. 1pt. +68 tuns 3hhd. 57gal. 2qt. 1pt. 87 tuns 3hhd. 45gal. 3qt. 1pt. +47 tuns 2hhd. 59gal. 3qt. 1pt. 47 tuns 3hhd. 39gal. 2qt. 1pt.

Ans. 354 tuns Ohhd. 30gal. 1qt. 19. Required the value of 67hhd. 15gal. 3qt. 1pt. 16hhd. 16gal. 3qt. 39hhd. 16gal. 3qt. + 47hhd. 62gal. 1qt. 1pt. + 43hhd. 57gal. 3qt. +71hhd. 61gal. 3qt. 1pt.

20. Add together of beer measure 161hhd. 53gal. 3qt. 1pt.; 371hhd. 52gal. 3qt. 1pt.; 98hhd. 19gal. 1qt.; 47hhd. 43gal. 1qt. Opt.; 61hhd. 43gal. 1qt. 1pt.; and 42hhd. 27gal. 3qt. 1pt.

21. Find the amount of 37bu. 3pk. 5qt. 1pt. +61bu. 2pk. 7qt. 1pt.32bu. 3pk. 2qt. + 71bu. 1pk. 6qt. 1pt. +61bu. 1pk. 3qt. 1pt. + 32bu. 3pk. 3qt. 1pt.

Ans. 298bu. Opk. 4qt. 1pt. 22. Required the value of 31bu. 3pk. 3qt. + 31bu. 3pk. 1qt.16bu. 3pk. 1qt. + 15bu. 3pk. + 17bu. 3pk. 1qt. + 14bu. 3pk. 1qt.

23. Required the value of 57y. 11mo. 27d. 23h. 29m. 55s. +31y. 11mo. 18d. 19h. 19m. 39s. + 46y. 9mo. 23d. 17h. 28m. 56s. 43y. 10mo. 16d. 18h. 17m. 48s. + 32y. 9mo. 19d. 16h. 23m. 28s. + 14y. 1mo. 29d. 21h. 28m. 16s.

Ans. 227y. 7mo. 16d. 21h. 28m. 2s. 24. Required the value of 23w. 6d. 23h. 59m. 58s. + 51w. 3d. 18h. 51m. 17s. + 29w. 5d. 21h. 47m. 49s. + 28w. 4d.

23h. 56m. 18s. + 19w. 6d. 10h. 18m. 53s. + 86w. 1d. 20h. 40m. 51s.

25. Add together 4S. 29° 59' 59'; 6S. 17° 17′ 29′′; 11S. 16° 56′ 58′′; 9S. 13° 46′ 51′′; 5S. 27° 16′ 42′′; and 2S. 25° 17' 17". Ans. 5S. 10° 35′ 16′′.

26. Add together 11S. 11° 16' 51"; 6S. 6° 6' 16"; 9S. 14° 56′ 56′′; 3S. 29° 29′ 49′′; 9S. 17° 18′ 58′′; and 6S. 13° 13' 52"

NOTE. We divide the sum of the signs, in the last two questions, by 12, and write down the remainder only. Since the circumference of a circle cannot exceed 12 signs (Art. 143).

27. Bought of a London tailor a vest for 1£. 13s. 4d., a coat for 7£. 12s. 9d., pantaloons for 2£. 3s. 9d., and surtout for 9£. 8s. Od.; what was the whole amount?

Ans. 20£. 17s. 10d.

28. Bought a silver tankard, weighing 1lb. 8oz. 17pwt. 14gr., a silver can, weighing 1lb. 2oz. 12pwt., a porringer, weighing 11oz. 19pwt. 20gr.; and 3 dozen of spoons, weighing 1lb. 9oz. 15pwt. 10gr.; what was the whole weight?

Ans. 5lb. 9oz. 4pwt. 20 gr.

29. What is the weight of a mixture of 3tb 43 23 29 14gr. of aloe, 2b 73 63 19 13gr. of picra, and 1b 103 13 29 17gr. of saffron ? Ans. 7b 103 33 19 4 gr.

30. Sold 4 loads of hay; the first weighed 27cwt. 3qr. 18lb.; the second, 31cwt. 1qr. 15lb.; the third, 19cwt. 1qr. 15lb.; and the fourth, 38cwt. 2qr. 24lb.; what is the weight of the whole?

31. Bought 5 pieces of broadcloth; the first contained 17yd. 3qr. 2na.; second, 13yd. 2qr. Ina.; the third, 87yd. 1qr. 3na. ; the fourth, 27yd. 1qr. 2na.; and the fifth, 29yd. 1qr. 2na.; what was the whole quantity purchased?

Ans. 175yd. 2qr. 2na. 32. A pedestrian travelled, the first week, 371m. 3fur. 37rd. 5yd. 2ft. 10in.; the second week, 289m. 2fur. 18rd. 3yd. 1ft. 9in.; and the third week, 399m. 7fur. 3ft. 11in.; how many miles did he travel? Ans. 1060m. 5fur. 16rd. 5yd. 1ft. 33. A man has three farms; the first contains 186A. 3R. 14p.; the second, 286A. 17p.; and the third, 115A. 2R.; how much do they all contain? Ans. 588A. 1R. 31p.

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