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13. Purchased a farm of 500 acres for $ 17,876. I sold 127 acres of it at $ 47 an acre, 212 acres at $ 96 an acre, and the remainder at $ 37 an acre. What did I gain by my bargain?
Ans. $ 14,402. 14. There is a certain island 18 miles in circuit, which A and B undertake to travel round, both starting from the same point and going round in the same direction. When A has traveled 17 miles and B 7 miles, how far apart are
Ans. 8 miles. 15. If 15 men can reap a certain field in 5 days, how long will it take 1 man to reap the same? Ans. 75 days.
16. What number is that, which being multiplied by 24, the product divided by 10, the quotient multiplied by 2, 32 subtracted from the product, the remainder divided by 4, and 8 subtracted from the quotient, the remainder shall be 2 ?
Ans. 15. 17. From 126 + (16 + 4) X 2 take (48 + 2) + (34 X 6) = (17 5).
Ans. 125. 18. There are in the library of a certain school 683 books, which number will give 23 books to each pupil, and 16 books over; what is the number of pupils ?
19. R. Howland in making a journey, after walking 12 miles and travelling 40 miles by stage, went by steamboat 5 times the distance he had travelled by stage, and by cars 6 times as far as he had walked, and 7 miles besides. What was the length of his journey?
Ans. 331 miles. 20. At an election A and B were candidates for the same office, and the whole number of votes cast for them was 9891, of which В received 1211 majority. What number of votes did each receive?
Ans. A, 4340 ; B, 5551. 21. The product of 3 numbers is 4080; one of the numbers is 15, and another 16. What is the third number?
22. How many tons of coal at 6 dollars a ton will be required to pay for 17 yards of cloth at 4 dollars a yard and 32 bushels of wheat at 2 dollars a bushel ? Ans. 22 tons.
23. James Cooper has manufactured in 4 years 5608 pairs of shoes, making each successive year 100 pairs more than the year before ; how many pairs did he manufacture each year?
Ans. 1252 ; 1352 ; 1452 ; 1552.
Ans. 4 years.
24. How many years will it take a young man earning 45 dollars, and spending 35 dollars of it, every month, if he have already 620 dollars, to lay up enough more to pay for a house costing 1100 dollars ?
25. If the product of the divisor by the quotient be 19782, and the remainder 31, what is the dividend ? Ans. 19813.
26. John Franklin purchased railroad stock to the amount of 4473 dollars, and sold a part of it for 1885 dollars, obtaining 65 dollars a share, which was at a loss of 6 dollars on every share sold; but the stock advancing much in value, he was able to dispose of the balance so as to gain by the whole operation 812 dollars. What did he get a share for the balance of the stock?
Ans. 100 dollars.
UNITED STATES MONEY.
ART. 100. UNITED States Money is the legal currency of the United States. It was established by Congress in 1786. Its denominations and their relative values are shown in the following
In accounts and ordinary business transactions, the only denominations mentioned are dollars and cents, eagles being expressed as dollars, dimes as cents, and mills as a fraction of a cent.
The dollar is the integer, or unit of measure of United States money; and therefore dimes are tenths of a dollar; cents, hundredths ; and mills, thousandths.
101. Parts of a dollar, or any quantity thus expressed, in tenths, hundredths, etc., are termed DECIMALS, or fractions, whose denominator (Art. 68) is 1, with one or more ciphers annexed. They are usually expressed by simply writing the numerator (Art. 68) with a point (.) before it, called the decimal point, or separatrix ; the first place at the right of the point being tenths ; the second place, hundredths ; the third place, thousandths; the fourth place, ten-thousandths; and so
Thus, io is written .1; ido is written .01 ; Toto is written .001; totoo is written .0001, etc.
102. In writing dollars and cents together, the decimal point or separatrix is placed between the dollars and the cents or decimal part ; and 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 before them, in the place of dimes. Thus, $ 30.375 is read, thirty dollars thirty-seven cents five mills, or thirty dollars and three hundred seventy-five thousandths of a dollar ; $ 12.05 is read, twelve dollars five cents, or twelve dollars and five hundredths of a dollar, etc.
103. The denominations of United States Money increasing from right to left, and decreasing from left to right, in the same manner as do thc units of the several orders in simple whole numbers, they may therefore be added, subtracted, multiplied, and divided according to the same rules.
104. The coins of the United States are of gold, silver, nickel, and bronze.
The gold coins are the double eagle, eagle, half-eagle, quarter-eagle, three-dollars, and dollar.
The silver coins are the dollar, half-dollar, quarter-dollar, dime, half-dime, and three-cent-piece.
The nickle coin is a three-cent-piece. The bronze coins are the cent and two-cent-piece. NOTE. All the gold and silver coins of the United States are now made of one purity, 9 parts of pure metal and 1 part alloy. The alloy for the silver is copper, and that for the gold 1 part copper and 1 part silver. The cent and two-cent-piece, by the law of 1864, are composed of 95 parts of pure copper and 5 parts of tin and zinc.
The standard weight of the eagle, as fixed by present laws, is 258 grains Troy, and the gold coins in proportion according to their values. The weight of the silver dollar is 4122 grains; half-dollar, 192 grains; quarter-dollar, 96
grains ; dime 38% grains; half-dime, 19; grains; three-cent piece, 11 grains; the cent, old coinage, 168 grains; the cent, new coinage, 48 grains.
The weight of the silver dollar, it will be seen, is greater in proportion to its value than the other silver coins. This is owing to their standard weight having been reduced, while that of the dollar remained unchanged; but since this reduction of weight of the smaller silver coins, no more of the silver dollar appear to have been coined. In circulation, the gold dollar, which of late years has been extensively coined, has almost entirely taken the place of the silver dollar.
The symbol $, or dollar sign, represents, probably, the letter U written upon au S, denoting U. S. (United States).
REDUCTION OF UNITED STATES MONEY.
105. REDUCTION of United States Money is changing the units of one of its denominations to the units of another, either of a higher or lower denomination, without altering their value.
106. To reduce units from a higher denomination to a lower. Ex, 1. Reduce 58 dollars to cents and mills.
Ans. 5800 cents; 58000 mills.
We multiply the 58 by 100, be5 800 cents.
cause 100 cents make 1 dollar; and 10
multiply the 5800 by 10, because
10 mills make 1 cent. Hence, 580 00 mills. Or thus: 58000 mills. To reduce dollars to cents, annex two ciphers; to 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.
107. To reduce units from a lower denomination to a higher. Ex. 1. Reduce 58000 mills to cents and to dollars.
Ans. 5800 cents; 58 dollars.
10) 58000 mills. 100) 5 800 cents.
We divide the 58000 by 10, because 10 mills make 1 cent; and divile the 5800 by 100, because 100 cents make 1 dollar. Hence,
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 off THREE figures.
EXAMPLES. 2. Reduce $ 765 to cents. 3. Change 726 mills to cents.
Ans. 728 cents. 4. How many dollars are 329 cents ? Ans. $ 3.29. 5. Change 12345 mills to dollars.
Ans. $ 12.345. 6. Reduce $123.56 to mills.
Ans. 123560 mills. 7. Reduce 2 eagles, 2 dollars, and 2 dimes to cents.
Ans. 2220 cts.
ADDITION OF UNITED STATES MONEY.
108. Ex. 1. Add together 17 dollars 13 cents 5 mills ; 8 dollars 4 cents 6 mills; 63 dollars 20 cents 3 mills; and 29 dollars 87 cents mills.
Ans. $ 118.259.
1 7.1 3 5
We write units of the same denomina8.0 4 6
tion in the same column, and add as in 6 3.2 0 3
addition of simple numbers (Art. 45), and
separate the dollars from the cents in the 2 9.8 7 5
answer by the decimal point. Ans. 11 8.2 5 9
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 decimal point directly under that above.
Proof. - The proof is the same as in addition of simple numbers.