23. Paid 1012 £. 10 s. for a principal of 750 £. taken in 7 years before; at what rate per cent. per annum did I pay interest? 24. Suppose there are 4 companies, in each of which there are 9 men; it is required to find how many ways 4 men may be chosen, one out of each company. 25. How many different numbers can be made of the following figures: 1220005555? 26. A and B began to play together with equal sums of money; A first won 20 guineas, but afterwards lost back of what he then had, when B had 4 times as much as A; what sum did each begin with? 27. What is the 30th power of 4? 28. A person after spending and of his money, has yet remaining 160 £.; what had he at first? 29. How much gold of 15, 17, and 22 carats fine, must be mixed with 5 oz. of 18 carats fine, so that the composition may be 20 carats fine? 30. If 18 ells of stuff that is yd. wide cost 39 s. 6 d., what will 50 ells, of the same quality, cost, being a yard wide? 31. The diameters of two concentric circles being 10 and 6, required the area of the ring contained between their circumferences. 32. What is the area of a triangle, whose base is 20 rods, and perpendicular 14 rods? 33. What is the area of a parallelogram, whose base is 12 rods, and perpendicular 40 feet? 34. The sun's diameter is 883217.58 English miles; Jupiter's is 89170.81; Saturn's 79042.35; Georgium Sidus's 35109; Mercury's 3222.48; Venus's 7687.85; Earth's 7964.12; Mars's 4189.69; and the Moon's 2180. Required the comparative magnitude between each of these bodies and the Earth. PART III. 12 EXPLANATION OF CHARACTERS. The sign of equality: as 12 d. 1 shilling, signifies that pence are equal to one shilling. Sign of addition: as 5+7=12, that is 5 added to 7 is equal to 12. Sign of subtraction; as 12-7=5; that is, 12 decreased by 7 is equal to 5. Read 12 minus 7, or 12 less 7 equal to 5. X Sign of multiplication: as 8X4-32; that is, 8 multiplied by 4 is equal to 32. or 5)30 Sign of division: as 305-6; that is, 30 divided by 5 is equal to 6. 240 Numbers placed in the manner of fractions, also denote division. The numerator, or upper number, is the dividend, and the denominator, or lower number, is the divisor: thus 240 is the same as 240-16=15. :: Sign of proportion; thus, 2:4:8: 16; that is, as 2 is to 4, so is 8 to 16. Sign of Geometrical progression. 9-2+6=13; that is, the difference between 9 and 2 added to 6 is equal to 13. and 2 is called a vinculum. which it is drawn. The horizontal line over the 9 12—3+4-5 Signifies, that the sum of 3 and 4 taken from 12 leaves, or is equal to 5. Prefixed to any number signifies that the square root of that number is required. Prefixed to any number signifies that the cube root of that number is required. 172 MONEY, WEIGHTS, MEASURES, &c. Before proceeding to the succeeding sections, the learner should make himself familiar with the following tables of Money, Weights, and Measures, &c. By doing this, he will greatly facilitate his future progress, and render the exercises more pleasant and interesting. 1. Federal Money. 10 Mills 10 Cents 10 Dimes 10 Dollars make one Dime d. $ 1000 100= 10 1 dollar. The right hand division of this table shows the number of mills, cents, &c. contained in a dime, &c.; thus 10000 mills, 1000 cents, or 100 dimes, or 10 dollars are equal to 1 eagle. Three kinds of metal gold, silver, and copper. are coined in the United States, The coins are the following :— Dollar, Dime, 2. English Money. Note. By this weight are weighed gold, silver, jewels, electuaries, and all liquors. An ounce of gold is divided into 24 parts, called carats; and an ounce of silver into 20 parts, called pennyweights ; therefore, to distinguish the fineness of metals, such gold as will lose nothing by fire, is said to be 24 carats fine. But if it lose 1 or more carats by fire, it is called 23 carats fine, or less, according to the loss sustained. Silver, which loses nothing by fire, is 12 ounces fine. If it lose 1 or more pennyweights in a pound by trial, it is said to be 11 oz. 19 pwts. fine, or less as the case may be. Alloy is some base metal, with which gold or silver is mixed to abate its fineness: 22 carats of gold, and 2 of copper are the standard of gold coin in England; and 11 oz. 2 pwts. of fine silver melted with 18 pwts. of copper, make the standard of silver coin. 28672 28= 1 Quarter. 1792 112 4 1 Hundred wt. 573440-35840-2240-80-20-1 Ton. By this weight are weighed all coarse and drossy goods, and metals, except gold and silver. 12 particular things make 12 doz. 1 dozen, 1 gross, a great gross, 200 lbs. 200 196 256 30 112 56 94 112 1120 19 cwt. 14 lbs. A Punch of foreign Prunes A Tother of foreign Lead A Stone of Iron, shot, or horseman's wt. 66 Butcher's Meat Note.-175 Troy ounces are just equal to 192 Avoirdupois ounces; and 175 Troy pounds are equal to 144 Avoirdupois. 1 lb. Troy=5760 grs.; and 1 lb. Avoirdupois=7000 grains. All weights used by Apothecaries above grains are Avoirdupois. The Apothecaries' ounce and pound are the same as the Troy, only differently divided. Scotch and Irish linens are bought by the English or American yard, which is the same, and Dutch linens by the Ell Flemish; but are sold in America by the American yard, and in England by the Ell English. Irish linens are sold there as in America. one English yard in every score of yards. The Scotch and The Scotch allow marked bar. in. ft. |