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24. The sum of two numbers.is 5482, and the smaller number is 1962 ; what is the larger ?
Ans. 3520. 25. The difference between two numbers is 125, and the omaller number is 1482 ; what is the greater ?
Ans. 1607. 26. The difference between two numbers is 1282, and the greater number is 6958; what is the smaller ? Ans. 5676.
27. If the dividend is 21775, and the divisor 871, what is the quotient ?
Ans. 25. 28. If the quotient is 482, and the divisor 281, what is the dividend ?
Ans. 135442. 29. If 144 inches make 1 square foot, how many square
feet in 20736 inches ?
Ans. 144 feet. 30. An acre contains 160 square rods ; how many square rods in a farm containing 769 acres ?
Ans. 123040 rods. 31. A gentleman bought a house for three thousand fortyseven dollars, and a carriage and span of horses for five hundred seven dollars. He paid at one time two thousand seventeen dollars, and at another time nine hundred seven dollars. How much remains due ?
Ans. 630 dollars. 32. The erection of a factory cost 68,255 dollars ; supposing this sum to be divided into 365 shares, what is the value of each?
Ans. 187 dollars. 33. Bought two lots of wild land; the first contained 144 acres, for which I paid 12 dollars per acre; the second contained 108 acres, which cost 15 dollars per acre. I sold both lots at 18 dollars per acre ; what was the amount of gain ?
Ans. 1188 dollars. 34. Sold 17 cords of oak wood at 6 dollars per cord, 36 cords of maple at 3 dollars per cord, and 29 cords of walnut at 7 dollars per cord. What was the amount received ?
Ans. 413 dollars. 35. Daniel Bailey has a fine farm of 300 acres, which cost him 73 dollars per acre. He sold 83 acres of this farm to Minot Thayer, for 97 dollars per acre; 42 acres to J. Russel, for 87 dollars per acre ; 75 acres to J. Dana, at 75 dollars per acre ; and the remainder to J. Webster, at 100 dollars per acre.
What was his net gain ?
Ans. 5430 dollars. 36. J. Gale purchased 17 sheep for 3 dollars each, 19 cows at 27 dollars each, and 47 oxen at 57 dollars each. He sold his purchase for 3700 dollars. What did he gain ?
Ans. 457 dollars. 37. Purchased 17 tons of copperas at 32 dollars per ton. I sold 7 tons at 29 dollars per ton, 8 tons at 36 dollars per ton, and the remainder at 25 dollars per ton. Did I gain or lose, and how much?
Ans. 3 dollars, loss. 38. John Smith bought 28 yards of broadcloth at 5 dollars per yard ; and, having lost 10 yards, he sold the remainder at 9 dollars per yard. Did he gain or lose, and how much?
Ans. 22 dollars, gain. 39. Which is of the greater value, 386 acres of land at 76 dollars per acre, or 968 hogsheads of molasses at 25 dollars per hogshead ?
Ans. The land, by 5136 dollars. 40. Bought of J. Low 37 tons of hay at 18 dollars per ton. I paid him 75 dollars, and 12 yards of broadcloth at 4 dollars per yard. How much remains due to Low ?
Ans. 543 dollars. 41. A purchased of B 40 cords of wood at 5 dollars per cord, 9 tons of hay at 17 dollars per ton, 19 grindstones at 2 dollars apiece, 37 yards of broadcloth at 4 dollars per yard, and 16 barrels of flour at 6 dollars per barrel ; what is the amount of A's bill?
Ans. 635 dollars. 42. John Smith, Jr., bought of R. S. Davis 18 dozen of National Arithmetics at 6 dollars per dozen, 23 dozen of Mental Arithmetics at 1 dollar per dozen, 17 dozen Family Bibles at 3 dollars per copy; what was the amount of the bill ?
Ans. 743 dollars. 43. R. Hasseltine sold to John James 169 tons of timber at 7 dollars per ton, 116 cords of oak wood at 6 dollars per cord, and 37 cords of maple wood at 5 dollars per cord ; James has paid Hasseltine 144 dollars in cash, and 23 yards of cloth at 4 dollars per yard; what remains due to Hasseltine ?
Ans. 1828 dollars. 44. J. Frost owes me on account 375 dollars, and he has paid me 6 cords of wood at 5 dollars per cord, 15 tons of hay at 12 dollars per ton, and 32 bushels of rye at 1 dollar per
bushel. How much remains due to me?
Ans. 133 dollars. 45. Gave 169 dollars for a chaise, 87 dollars for a harness, and 176 dollars for a horse. I sold the chaise for 187 dollars, the harness for 107 dollars, and the horse for 165 dollars. What sum have I gained ?
Ans. 27 dollars. 46. Bought a farm of J. C. Bradbury for 1728 dollars, for which I paid him 75 barrels of flour at 6 dollars per barrel, 9 cords of wood at 5 dollars a cord, 17 tons of hay at 25 dollars a ton, 40 bushels of wheat at 2 dollars a bushel, and 65 bushels of beans at 3 dollars a bushel ; how many dollars remain due to Bradbury?
Ans. 533 dollars.
UNITED STATES MONEY.
68. United States Money, established by Congress in 1796, is the legal currency of the United States.
16 Mills make 1 Cent, marked
10000 Simple Numbers, that is, numbers whose units are all of a single kind or denomination, have thus far been made use of in this work. The units or denominations of United States
increase from right to left, and decrease from left to right, in the same manner as do the units of the several orders in simple numbers ; and may, therefore, be added, subtracted, multiplied, and divided in like manner as simple numbers.
Dollars are separated from cents by a point (.) called a separatrix or decimal point; the first two places at the right of the point being cents; and the third place, mills. Thus, $ 16.253 is read, sixteen dollars, twenty-five cents, three mills.
Since cents occupy two places, the place of dimes and of cents, when the number of cents is less than 10, a cipher must be written in the place of dimes; thus, .03, .07, &c.
The Coins of the United States consist of the double-eagle, eagle, half-eagle, quarter-eagle, three dollars, and dollar, made of gold; the dollar, half-dollar, quarter-dollar, dime, half-dime, and three-cent piece, made of silver ; a three-cent piece, made of nickel ; the cent and two cent pieces, made of bronze.
NOTE 1.--Mill is from the Latin word mille (one thousand); Cent, from centum (one hundred); Dime, from a French word signifying a tithe or tenth.
68. What is United States money? Repeat the table of United States money. What is a simple number? The denominations of United States money? How do they increase from right to left? How are they added, subtracted, multiplied, and divided? How are dollars separated from cents and mills ? Why must a cipher be placed before cents, when the number is less than 10? Why are two places allowed for cents, while only one is allowed for mills ? Name the coins of the United States.
The term DOLLAR is said to be derived from the Danish word Daler, and this from Dale, the name of a town, where it was first coined.
The symbol $ represents, probably, the letter U written upon an S, denoting U. S. (United States.)
NOTE 2.- All the gold and silver coins of the United States are now made of one purity, nine parts of pure metal, and one part alloy. The alloy for the silver is pure copper; and that for the gold, one part copper and one part silver. The cent and two cent pieces are now made of 95 parts of copper and 5 parts tin and zinc.
The standard weight, as fixed by present laws, of the eagle, is 258 grains, Troy; the silver dollar, 4125 grains; half-dollar, 192 grains; quarterdollar, 96 grains ; dime, 38grains; half-dime, 19} grains; silver three cent piece, 115m grains; and the cent, new coinage, 48 grains.
Note 3. – The currency of Canada, Nova Scotia, and New Bruns. wick, like that of the United States, has for its unit the dollar, consisting of 100 cents.
REDUCTION 69. Reduction of United States Money is changing the units of one of its denominations to units of another, of equal value.
70. To reduce from a higher to a lower denomination. Ex. 1. Reduce 25 dollars to cents and mills.
Ans. 2500 cents, 25000 mills. OPERATION. 25 dollars. 100
We multiply the 25 by 100, be2 5 0 0 cents.
cause 100 cents make 1 dollar; and
multiply the 2500 by 10, because 10 10
mills make 1 cent. 2 5 0 0 0 mills. Or thus, 2 5 0 0 0 mills.
RULE. To reduce dollars to cents, annex two ciphers; 10 reduce dollars to mills, annex THREE ciphers; and to reduce cents to mills, annex ONE cipher.
Note. — Dollars, cents, and mills, expressed by a single number, are reduced to mills by merely removing the separating point; and dollars and cents, by annexing one cipher and removing the separatrix.
71. To reduce from a lower to a higher denomination. Ex. 1. Reduce 25000 mills to cents and dollars.
Ans. 2500 cents, $ 25.
69. What is reduction of United States Money? - 70. What is the rule for reducing dollars to cents and mills ? The reason for the rule? How do you reduce dollars and cents to cents, or dollars, cents, and mills, to mills ? The reason for this rule ?
10) 25 0 0 0 mills.
We divide the 25000 by 10, because 100) 2500 cents. 10 mills makes 1 cent; and divide the
2500 by 100, because 100 cents make 2 5 dollars. 1 dollar. Or thus, 2 510 00 mills.
RULE. To reduce mills to cents, cut off ONE figure on the right; to reduce cents to dollars, point off two figures; and to reduce mills to dollars, point of THREE figures.
EXAMPLES FOR PRACTICE.
1. Reduce $ 125 to cents.
Ans. 12500 cents.
Ans. $ 0.297.
Ans. $ 41.23.
72. RULE. — Write dollars, cents, and mills, so that units of the same denomination shall stand in the same column.
Add as in addition of simple numbers, and place the separating point directly under that above.
Proof. — The proof is the same as in addition of simple numbers.
EXAMPLES FOR PRACTICE.
cts. m. 4 5.2 43 1 3.8 9 6 9 3.5 1 6 5 2.3 4 3
147.8 6 7 8 9.5 8 49 6.3 7 911.34
Ans. 2 0 4.9 98
19 4.6 6 9
14 6.4 3 6
2 3 4 5.1 5
71. What is the rule for reducing mills to cents ? For cents to dollars ? Mills to dollars? The reason for each ? - 72. How must the numbers be written down in addition of United States money? How added? How pointed off? The rule ?