18. John is 18 years old, and his age is of his sister's age. How old is his sister? 19. A speculator paid $64283 for 1351 acres of land. How much did it cost him per acre? 20. I sold of a flock of 18 sheep for $263. What was the price per head for the sheep? 21. A has $40 which is 14 times B's money. dollars has B? How many 22. I bought three pieces of carpet at $14 per yard. One piece contained 40 yards, another 33 yards, the other 3512 yards. What was the entire cost? 23. A merchant bought 9 dozen eggs at $3 per dozen and paid for them in cloth worth $ per yard. How many yards of cloth did it require? 24. The product of two fractions is, and one of the fractions is. What is the other fraction? 25. If the dividend is 1 and the divisor is, what is the quotient? 26. If 2 barrels of flour cost $261, what will 8 barrels cost? 27. A and B worked for a certain sum. A worked 4 days and received $63. How much did B receive if he worked 53 days at the same rate? 28. A farmer sold of his sheep to one man and to another, when he found that he had 140 sheep left. How many had he at first? 29. A bought 150 tons of hay. He sold 35 tons at $43 per ton, 40 tons at $5 per ton and 3 of the remainder at $5 per ton. How much money did he receive? 30. How many yards of cloth at $3 per yard must be given for 15 tons of coal at $41 per ton? 31. In how many days will 3 horses eat 4 bushels of oats if each horse eats of a bushel each day? 32. How many pounds of butter at $ per pound will pay for 48 bushels of corn at $3 per bushel? 33. A man paid $3500 for a farm and cost of the house which he built upon it. farm and house together. this was 2 times the Find the cost of the 34. With $13 I bought of 2 of § of a yard of cloth. At that rate what will 3 yards cost? 35. A merchant paid $25 for 50 gallons of molasses. He lost by leakage and sold 20 gallons at $3. The remainder was sold so as to gain $5 on the whole. Find the selling price per gallon. 36. How many yards of cloth yards wide will line 23 yards, 1 yards wide? 37. A speculator bought 367 bushels of wheat at $ per bushel; he sold 1263 bushels at $3 per bushel. He afterwards bought 260 bushels at $8 per bushel, and then sold all he had at $1 per bushel. What did he gain? 38. A and B own, if B owns own 280 horses. How many horses does each as many as A? 39. If 11 bushels of apples cost $416, what will be the cost of 19 bushels? 40. A stone mason worked 113 days, and after paying his board and other expenses with of his earnings, he had $20 left. How much did he receive a day? 41. What will 3 acres of land cost, if 63 acres cost $807? 42. How many yards of carpet yards wide will it require to carpet a room 7 yards long and 4 yards wide? 43. A and B together have $364. B's money is equal to of A's. How many dollars has each? 44. Lyman can do a piece of work in 4 days and Farwell can do it in 5 days. How long will it take them, working together, to do it? 45. S. P. Bruce bought 403 acres of land at $16 per acre. He sold 25 acres to James Collins at $221 per acre, and sold the remainder to D. E. White at $15 per acre. How much did Bruce pay for the land, how much did he receive for it, and what was his gain? 46. A can do a piece of work in 10 days; B, in 15 days; C, in 12 days. How long will it take them all to do the work? 47. A gentleman, having 271 acres of land, sold of it, and gave 3 of it to his son. What was the value of the remainder at $57 per acre? 48. A post stands in the mud, in the water, and 21 feet above the water; what is its length? 49. A and B together bought 680 sheep. A paid $9 as often as B paid $8. How many sheep should each receive? 50. Smith owning of a mill, sold of his share to Brown for $870. Find the value of the entire mill and Smith's share at present. 51. How many days will be required for A, B and C to do a piece of work, if A can do it in 20 days; B in 30 days; C in 25 days? 52. A and B together can do a piece of work in 4 days. A can do it alone in 6 days. How long will it take B to do it alone? 53. A partnership business realized a profit of $6160. What was each partner's gain, if A invested of the capital; B, 1; C, the remainder? 54. I sold two horses for $240. The selling price of one was of the selling price of the other. Find the selling price of each horse. 55. A dealer sold two cows for $24 each. He lost of the cost on one and gained of the cost of the other. Did he gain or lose and how much by the transaction? 56. A. C. Lamb bought a horse, buggy and harness. The cost of the horse was 14 the cost of the buggy, and the cost of the harness was the cost of the buggy. What was the cost of each, if the cost of the harness was $30? 57. A's money is of B's money; B's money; C's money is 13 times D's money. How much money has each, if of A's money is $64? How much have they together? money is of C's 58. How many times is of of 27 contained in of of 42? 59. A and B together own 792 cows; of A's number equals of B's number. How many cows does each own? 60. A father left his eldest son of his estate, his youngest son of the remainder, and his daughter the remainder, who received $1723§ less than the youngest son; what was the value of the estate? DECIMAL FRACTIONS 111. A Decimal Fraction is one which has for its denominator 10, 100, 1000, or 1 with any number of ciphers annexed, as 10, 100, 1830. 23 112. Common Fractions arise from dividing a unit into any number of equal parts as halves, thirds, fifths, etc. Decimal fractions arise from dividing a unit into ten equal parts called tenths; each of these parts may be divided again into ten equal parts called hundredths, etc. 113. Since the denominator of a decimal fraction is always 1 with ciphers annexed, it may be expressed by writing the numerator only and using the decimal point to indicate the denominator. 114. The Decimal Point is a period (.) which must always be placed at the left of the decimal. It is read "and." Thus 7.4 is read and 4 tenths. A number containing an integer and decimal is called a mixed decimal. 115. Decimal fractions like simple numbers increase in value from right to left and decrease from left to right. The first figure on the right of the decimal point is called tenths, the second hundredths, the third thousandths, etc. Thus, is expressed .1 and read one tenth. To is expressed .01 and read one hundredth. 000 1000 is expressed .125 and read one hundred twenty-five thousandths. 100 is expressed 100.025 and is read one hundred, and twenty-five thousandths. NOTE. Decimal fractions are usually called decimals, and common fractions merely fractions. |