The body weighing as much as the head and tail both, But x= 2 Now, if 18 added to the half of x gives x, 18 must itself be equal to , and twice 18, or 36, to x. Having found the value of x, we easily obtain the remaining values. The pupil may analyse the following examples, either with or without the aid of letters. 1. A father's age is 7 times that of his son, and the sum of their ages is 40. What is the age of each? 2. In a certain school there are 45 scholars, and there are twice as many boys as girls. Required the number of each? 3. A man performed a journey of 135 miles, going twice as far the second day as on the first, and three times as far the third day as on the second. How far did he travel each day? 4. A., B., and C., entered into partnership, contributing in the whole, $4833. B. paid twice as much as A., and C. paid twice as much as A. and B. How much did each contribute? 5. In a certain school of 70 scholars, three times as many study Arithmetic as study Latin, and twice as many learn to read, as study Arithmetic. How many are there in each study? 6. An estate of $7000 was so divided that the widow received $500 more than the daughter, and the son $1100 more than the widow. What was the share of each? 7. Divide the number 97 into four such parts that the second may be twice the first, the third 7 more than the second, and the fourth 18 more than the first. 8. A thief travels at the rate of 6 miles an hour, and after he has been absent 5 hours, a constable starts in pursuit, at the rate of 9 miles an hour. In what time will the thief be overtaken? 9. A man when he was married, was three times as old as his wife, but after they had lived together 15 years, he was only twice as old. How old was each at the time of marriage? 10. A farmer bought some cows and some calves for $461, giving $23 apiece for the cows, and $9 apiece for the calves, and there were twice as many calves as cows. How many were there of each? 11. At a certain election, the successful candidate had 163 votes more than his opponent, and the whole number of votes polled was 1125. How many did each receive? 12. What sum of money will yield $123.50 in 2 years, at 5 per cent. simple interest? 13. A gentleman distributed $1.95 among 3 beggars, giving the second 25 cents more than the first, and the third twice as much as the second. How much did each receive? 14. If from three times a certain number 17 be subtracted, the remainder will be 112. What is the number? 15. A's age is 24 times B's, and the sum of their ages Required the age of each. 49. is EXAMPLE FOR THE BOARD. A man being asked his age, replied, "If,,, and 3 of my age and 19 years more be added to my age, the sum will be 3 times my age.' What was his age? Let x his age. x 3x x + + + + + 19 = 30x 20x 15x 36x 3x, 5 + 60 60 60 60 After stating the question, we reduce all the fractions to a common denominator, and add them as in ordinary Addition of fractions. We then find that 16. A merchant owes two of his creditors $1575, and he owes the second but as much as the first. What is the amount of each debt? 10 5 17. In a certain school the boys learn to read, learn to write, learn Algebra, learn drawing, and the remaining 4 study Latin. How many are there in the school? 18. One-third of a certain pole is painted green, and of it is painted white, the remainder, which is 8 feet, being in the ground. What is the length of the pole? 19. A man going to market, was met by another, who said: "Good morrow, neighbor, with your hundred geese." He replied: "I have not a hundred; but if I had as many more, and half as many more, and two geese and a half, I should have a hundred." How many had he? 20. Three-sevenths of a certain number exceed of it by 24. What is the number? 21. A man bought 38 pounds of coffee and 95 pounds of sugar; he gave 2 cents per lb. more for the coffee than for the sugar, and the sugar cost twice as much as the coffee. What was the price of each per pound? 22. The age of a certain man when he was married, was to that of his wife, as 11 to 10; ten years afterwards the proportion was as 16 to 15. What was the age of each on the wedding day? 23. There are two numbers, such that if 21 be added to the first, the sum will be 5 times the second, and if 21 be added to the second, the sum will be 3 times the first. What are the numbers? 24. The sum of 1, 1, 1, and 4 of a certain number, is 575. Required the number. 25. The sum of three numbers is 96; the second is 2 more than the first, and the third is 4 more than the sum of the other two. What are the numbers? 26. Two stages are travelling towards each other, one at the rate of 52 miles an hour, the other 6 miles an hour. In what time will they meet, if they are now 383 miles apart? 27. Two men start from the same place and travel in opposite directions, one at the rate of 41 miles an hour, and the other 5 miles an hour. In what time will they be 100 miles apart? 11 28. A farmer hired a certain number of boys, and twice as many men, agreeing to pay each man 75 cents a day, and each boy 25 cents. The daily wages of the whole, amounted to $5.25. How many were there of each? What 29. A gentleman owns a carriage that cost him 3 times as much as his horse, and both together cost $720. was the price of each? 30. There is a number to which if 1 and of itself be added, the sum will be of 87 less than 16. What is the number? 31. What number is that from which if we deduct of itself, and of the remainder, there will be 18 left? 32. If A. can do of a do of it in 4 days, and what time will they all do piece of work in 5 days, B. can C. can do of it in 2 days, in of it by working together? 33. Divide 87 into two such parts that one may be as much above 393 as the other is less than 39. 34. There are two men of equal ages, but if one was 51⁄2 years older, and the other 94 years younger, the former would be twice as old as the latter. Required their ages. 35. If and of a certain number be added, 8 of the sum will be 1 greater than of 19. What is the number? 36. A man inquiring the distance to Boston, was told that if it was as far again and as far, and as far, it would be 3 miles less than 101 What was the distance? miles. 37. A laborer received $1.50 for every day he worked, and lost 50 cents every day he was idle. He worked twice as many days as he was idle, and at the end of the time, he received $42. How many days did he work? 38.5 and and and of a certain number, make 24. What is the number? 39. Of what number is 25, 93 less than of? 4 17 40. There is a pole painted blue, painted white, painted red, and 2 feet unpainted. What is the length of the pole? 41. If a man can do 5 of a piece of work in 3 days, and a boy can do & of it in 5 days, how long will it take them both to do the whole? 42. A farmer hired an equal number of men and boys, giving each man 75 cents, and each boy 37 cents. How many were there of each, the wages of the whole being $10.12? 43. What is the height of a steeple that casts a shadow of 763 feet, when a pole 9 feet high casts a shadow of 5 feet? |