which was I fourth of what he had ; how many had he? 3. A man paid away 4 dollars, which was 2 thirds of all the money he had; how much had he? 4. A man sold a watch for 18 dollars, which was 3 fourths of what it cost him; how much did it cost? 5. A man sold a cow for 15 dollars, which was 3 fifths of what the cow cost; how much did he lose by his bargain ? 6. A man bought 12 yards of cloth, and sold it for 54 dollars, which was 9 eighths of what it cost him; what did it cost him a yard ? and how much did he gain by his bargain ? 7. There is a pole standing in the water, so that 10 feet of it is above the water, which is 2 thirds of the whole length of the pole; how long is the pole? 8. There is a pole two thirds under water, and 4 feet out; how long is the pole? 9. There is a pole two fifths under water, and 6 feet out of the water ; how long is the pole? 10. There is an orchard, in which 3 sevenths of the trees bear cherries, and 2 sevenths bear peaches, and 10 trees bear plums; how many trees are there in the orchard ? and how many of each sort ? 11. There is a school, in which 2 ninths of the boys learn arithmetic, 3 ninths learn grammar, 1 ninth learn geography, 1 ninth learn geometry, and 12 learn to write ; how many are there in the school ? and how many attending to each study? 12. A man sold a watch for 63 dollars, which was y fifths of what it cost him; how much did he gain by the bargain? Miscellaneous Examples. 1. Ir 1 yard of cloth cost 4 dollars, what will 5 yards cost? 2. A man bought 3 pounds of raisins, at 9 cents a pound, and 16 oranges, at 4 cents apiece, and i pound of candles for 16 cents; what did they all come to? 3. A boy had 37 apples; he kept five himself, and divided the rest equally among four companions; how many did he give them apiece? 4. Two men are 40 miles apart, and both travel; ling the same way; the hindermost man gains upon the other 5 miles each day; in how many days will he overtake him ? 5. Two men are travelling the same way ; ope travels at the rate of 38 miles a day; the other, who is behind the former, travels 44 miles; how much iloes he gain of the first each day? and in how many days would he gain 60 miles? 6. A fox is 80 rods before a greyhound, and is running at the rate of 27 rods in a minute; the greyhound is following at the rate of 31 rods in a minute; in how many minutes will the greyhound overtake the fox ? 7. If 2 yards of cloth cost 6 dollars, what would 4 yards cost? what would 12 yards cost ? 8. If 8 sheep cost 24 dollars, what would 3 cost? 9. If 4 tons of hay will keep 3 horses through the winter, how many tons will keep 30 horses the same time? 10. If a man spends 8 shillings a day, how many dollars will he spend in a week ? 11. Bought 10 pieces of cloth, each containing 5 yards, for 100 dollars; what was it a piece ? and how much a yard? 12. If the wages of 12 weeks come to 60 dollars, what is that a month? and how much for 5 weeks? 13. If 7 horses eat 14 bushels of oats in 1 week, how many bushels would 15 horses eat in the same time? 14. If 3 horses eat 8 bushels of oats in 2 weeks, how long would it take them to eat 40 bushels ? 15. If i horse eat 1 bushel of oats in 3 days, in how many days would 4 horses eat 36 bushels ? 16. If 2 men spend 12 dollars in 1 week, how many dollars would 3 men, at the same rate, spend in 5 weeks? 17. If a staff 3 feet long cast a shadow of 2 feet at 12 o'clock, what is the length of a pole that casts a shadow 18 feet at the same time of day? 18. If 47 gallons of water, in 1 hour, run into a cistern containing 108 gallous, and by a pipe 38 gallons run out in an hour, how much remains in the cistern in an hour? and in how many hours will the cistern be filled ? 19. If 4 men can do a piece of work in 8 days, how many men would it take to do the same work in 4 days ? 20. If 6 men can do a piece of work in 9 days, in how many days would 2 men do it? 21. If 8 'men can do a piece of work in 5 days, in how many days would they do a piece of work 4 times as large? 22. If 7 men can do a piece of work in 3 days, how many men would it take to do a piece of work 5 times as large in the same time? 23. If 8. men can do a piece of work in 4 days, in how many days would 2 men do a piece of work one half as large? 24. A man bought a cask of wine containing 63 gallons, 3 sevenths of which leaked out; and he sold the remainder for 36 dollars; how much per gallon did he sell it for? 25. If a cask of wine cost 48 dollars, what is 5 eighths of it worth ? 26. A man bought 7 oranges for 6 cents apiece, and sold them all for 54 cents; how much did he gain by the bargain ? 27. A man bought 8 yards of cloth for 56 dollars, and sold it again for 9 dollars a yard; how much did he gain by the bargain ? 28. A man bought 8 barrels of flour for 40 dollars; how much must he sell it at per barrel to gain 16 dollars ? 29. A man bought five firkins of butter at 7 dollars a firkin ; how must he sell it per firkin to gain 10 dollars : 30. A man gave 35 cents for his breakfast, which was 5 eighths of what he gave for his dinner; what did he give for his dinner? 31. A ship's crew of 6 men have provision for 3 months; how many months would it last 1 man? 32. A ship's crew have provision sufficient to last 1 man 27 months; how long would it last 9 men? 33. A ship's crew have provision sufficient to last 3 men 10 months; how long would it last 5 men ? 34. A man built 40 rods of wall in a certain time, another man can build 9 rods while the first builds 5; how much would he build in the same time? SECTION VII. If the combinations in this section should be found too difficult, they may be omitted until reviewing the book. A. 1. A MAN, being asked the age of his eldest son, answered, that his youngest son was six years old, and that 2 thirds of the youngest son's age was just 1 fifth of the eldest son's age. Required the age of the eldest son. 2. 2 thirds of 6 is 1 fifth of what number: 3. A man, being asked how many sheep he had, said that he had them in two pastures; in one pasture he had eight; and that 3 fourths of these was just 1 third of what he had in the other. How many were there in the other? 4. 3 fourths of 8 is 1 third of what number? 5. Two boys talking of their ages, one said he was 9 years old. Well, said the other, 2 thirds of your age is exactly 3 fourths of my age, now, if you will tell me how old I am, I will give you as many apples as I am years old. What was his age ? 6. 2 thirds of 9 is 3 fourths of what number? 7. Two boys counting their money, one said his had ten cents. The other says, 4 fifths of you inoney is exactly 2 sevenths of mine; now, if you will tell how many I have, I will give you 1 half of them. How many had he? 8. 4 fifths of 10 is 2 sevenths of what number: 9, 5 sixths of 12 is 2 thirds of what number? 10. 6 sevenths of 14 is 4 ninths of what number? 11. 6 fifths of 15 is 2 thirds of what number? 12. my ninths of 18 is 2 fifths of what number? 13. 4 fifths of 20 is 8 sevenths of what number? 14. 8 sevenths of 21 is 6 tenths of what number? 15. 5 sixths of 24 is 10 sevenths of how many times 5 ? 16. 3 sevenths of 28 is 2 eighths of how many times 7 ? 17. 4 fifths of 30 is 6 sevenths of how many times 8? 18. 6 eighths of 32 is 8 ninths of how many times 5? |