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5. The sum of two numbers is 48, and one of the numbers is 19; what is the other?
6. The greater of two numbers is 29, and their difference 10; what is the less number?
7. The less of two numbers is 19, and their difference is 10; what is the greater?
8. A man bought 5 pieces of cloth, at 44 dollars a piece; 974 pairs of shoes, at 3 dollars a pair; 600 pieces of calico, at 6 dollars a piece; what is the amount?
9. A man sold six cows, worth fifteen dollars each, and a yoke of oxen, for 67 dollars; in pay, he received a chaise, worth 124 dollars, and the rest in money; how much money did he receive?
10. What will be the cost of 15 pounds of butter, at 13 cents per pound?
11. How many bushels of wheat can you buy for 487 dollars, at 2 dollars per bushel?
¶ 24. When the price of one pound, one bushel, &c. of any commodity is given, how do you find the cost of any number of pounds, or bushels, &c. of that commodity? If the price of the 1 pound, &c. be in cents, in what will the whole cost be? If in dollars, what? if in shillings?
if in pence? &c.
When the cost of any given number of pounds, or bushels, &c. is given, how do you find the price of one pound or bushel, &c. In what kind of money wil the answer be? When the cost of a number of pounds, &c. is given, and also the price of one pound, &c., how do you mind the number of pounds, &c.
12. When rye is 84 cents per bushel, what will be the cost of 948 bushels? how many dollars will it be?
13. If 648 pounds of tea cost 284 dollars, (that is, 28400 cents,) what is the price of one pound?
When the factors are given, how do you find the product? When the product and one factor are given, how do you find the other factor?
When the divisor and quotient are given, how do you find the dividend?
When the dividend and quotient are given, how do you find the divisor?
14. What is the product of 754 and 25?
15. What number, multiplied by 25, will produce 18850? 16. What number, multiplied by 754, will produce 18850? 17. If a man save six cents a day, how many cents would he save in a year, (365 days,)? how many in 45 years? how many dollars would it be? how many cows could he buy with the money, at 12 dollars each?
Ans. to the last, 82 cows, and 1 dollar 50 cents remainder.
18. A boy bought a number of apples; he gave away ten of them to his companious, and afterwards bought thirty-four more, and divided one half of what he then had among four companions, who received 8 apples each; how many apples did the boy first buy?
Let the pupil take the last number of apples, 8, and reverse the process. Ans. 40 apples.
19. There is a certain number, to which, if 4 be added, and 7 be subtracted, and the difference be multiplied by 8, and the product divided by 3, the quotient will be 64; what is that number? Ans. 27. 20. A chess board has 8 rows of 8 squares each; how many squares on the board?
25. 21. There is a spot of ground 5 rods long, and 3 rods wide; how many square rods does it contain ?
Note. A square rod is a square (like one of those in the annexed figure) measuring a rod on each side. By an inspection of the figure, it will be seen, that there are as many squares in a row as rods on one side, and that the number of rows
is equal to the number of rods on the other side; therefore, 315, the number of squares.
Ans. 15 square rods.
A figure like A, B, C, D, having its opposite sides equal and parallel, is called a parallelogram or oblong.
22. There is an oblong field, 40 rods long, and 24 rods wide; how many square rods does it contain?
23. How many square inches in a board 12 inches long, and 12 inches broad? Ans. 144.
24. How many square feet in a board 14 feet long and 2 feet wide?
25. A certain township is six miles square; how many square miles does it contain ? Ans. 36.
26. Aman bought a farm for 22464 dollars; he sold one half of it for 12480 dollars, at the rate of 20 dollars per acre; how many acres did he buy? and what did it cost him per acre?
27. A boy bought a sled for 86 cents, and sold it again for 8 quarts of walnuts; he sold one half of the nuts at 12 cents a quart, and gave the rest for a penknife, which he sold for 34 cenis; how many cents did he lose by his bargains?
28. In a certain school-house, there are 5 rows of desks; in each row are six seats, and each seat will accommodate 2 pupils; there are also 2 rows, of 3 seats each, of the same size as the others, and one long seat where 8 pupils may sit; how many scholars will this house accommodate? Ans. 80.
29. How many square feet of boards will it take for the floor of a room 16 feet long, and 15 feet wide, if we allow 12 square feet for waste?
30. There is a room 6 yards long and 5 yards wide; how many yards of carpeting, a yard wide, will be sufficient to cover the floors, if the hearth and fireplace occupy 3 square yards?
31. A board, 14 feet long, contains 28 square feet; what is its breadth?
32. How many pounds of pork, worth 6 cents a pound, can be bought for 144 cents?
33. How many pounds of butter, at 15 cents per pound, must be paid for 25 pounds of tea, at 42 cents per pound?
34. 4+5+6+1+8=how many?
35. 4+3+10-2-4-6-7= how many?
(4) of 3? of 45674312?
36. A man divides 30 bushels of potatoes among 3 poor men; how many bushels does each man receive? What is of thirty? How many are 3 (two thirds) of 30? 37. How many are one third - of 9? of 282 ? 38. How many are two thirds of 9 ? of 282 ? 39. How many are of 40? 60? of 60? - 1 of 80 ? 246876 ? of 246876 ? 40. How many is of 80? 41. An inch is one twelfth part (1) of a foot; how many
(3) of 3?
of 80 ?
2 of 40?
feet in 12 inches?
in 24 inches?
in 12243648 inches?
42. If 4 pounds of tea cost 128 cents, what does 1 pound cost? 2 pounds? 3 pounds? 5 pounds? 100 pounds?
in 36 inches?
43. When oranges are worth 4 cents apiece, how many can be bought for four pistareens, (or 20 cent pieces?)
44. T earth, in moving round the sun, travels at the rate of 68000 miles an hour; how many miles does it travel in one day, (24 hours?) how many miles in one year, (365 days?) and how many days would it take a man to travel this last distance, at the rate of 40 miles a day? how many years? Ans. to the lust, 40800 years. earn in 20 weeks, at 80 cents
45. How much can a man per day, Sundays excepted?
46. A man married at the age of 23; he lived with his wife 14 years; she then died, leaving him a daughter, 12 years of age; 8 years after, the daughter was married to a man 5 years older than herself, who was 40 years of age when the father died; how old was the father at his death? Ans. 60 years
47. There is a field 20 rods long, and 8 rods wide; how many square rods does it contain ? Ans. 160 rods.
48. What is the width of a field, which is 20 rods long, and contains 160 square rods ?
49. What is the length of a field, 8 rods wide, and containing 160 square rods?
50. What is the width of a piece of land, 25 rods long; and containing 400 square rods?
26. A number expressing things of the same kind is called a simple number; thus, 100 men, 56 years, 75 cents, are each of them simple numbers; but when a number expresses things of different kinds, it is called a compound number; thus, 43 dollars 25 cents and 3 mills, is a compound number; so 4 years 6 months and 3 days, 46 pounds 7 shillings and 6 pence, are compound numbers.
Note. Different kinds, or names, are usually called di ferent denominations.
Federal money is the coin of the United States. The kinds, or denominations, are eagles, dollars, dimes, cents, and mills.
= 1 dime.
10 cents, (=100 mills,) 10 dimes, 100 cents 10 dollars, (=100 dimes
= 1 dollar.
1000 cents=10000 mills) = 1 eagle.* SIGN. This character, $, placed before a number, shows it to express federal money.
As 10 mills make a cent, 10 cents a dime, 10 dimes a dollar, &c. it is plain, that the relative value of mills, cents, dimes, dollars and eagles corresponds to the orders of units, tens, hundreds, &c. in simple numbers. Hence, they may be read either in the lowest denomination, or partly in a higher, and partly in the lowest denomination. Thus:
are equal to
4652 may be read, 34652 mills; or 3465 cents and 2 mills; or, reckoning the eagles tens of dollars, and the dimes tens of cents, which is the usual practice, the whole may be read, 34 dollars 65 cents and 2 mills.
For ease in calculating, a point () called a separatrix,† is placed between the dollars and cents, showing that all the figures at the left hand express dollars, while the two first figures at the right hand express cents, and the third, mills. Thus, the above example is written $34'652; that is, 34 dollars 65 cents 2 mills, as above. As 100 cents make a dollar, the cents may be any number from 1 to 99, often requiring two figures to express them; for this reason, two places are appropriated to cents, at the right hand of the point, and if the number of cents be less than ten, requiring but one figure to express them, the ten's place must be filled with a cipher. Thus, 2 dollars and 6 cents are written 2'06. 10 mills make a cent, and consequently the mills never exceed 9, and are always expressed by a single figure. Only
The eagle is a gold coin, the dollar and dime are silver coins, the cent is a copper coin. The mill is only imaginary, there being no coin of that denomina Gon. There are half eagles, half dollars, half dimes, and half cents, real! coins:
The character used for the separutrix, in the "Scholars' Arithmetic," was the comma; the comma inverted is here adopted, to distinguish it from the con ma used in punctuation,