which was 1 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 be? 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 pble; 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 féet 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 7 fifths of what it cost him; how much did he gain by the bargain? Miscellaneous Examples. 1. IF 1 yard of cloth cost 4 dollars, what will 5 yards cost? 2. A man bought 3 pounds of raisins, at 7 cents a pound, and 16 oranges, at 4 cents apiece, and I pound of candles for 16 cents; what did they al. 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 travelling 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, one travels at the rate of 38 miles a day, the other, who . is behind the former, travels 44 miles ; how much does 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, 'now many dollars will he spend in a week? 11. Bought 10 pieces of cloth, each containing 5 yards, for 100 dollars; what was it apiece ? 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 " 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 i 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 9 shadow 18 feet at the same me time of day? 18. If 47 gallons of water, in 1 hour, run into a cistern containing 108 gallons, 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 s 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 ble 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 ? 23. A man bought 8 barrels of flour for 40 dollars; how much must he sell it at per barrel to gain 10 dollars ? 29. A man bought five firkins of butter at 7 dollars a firkin ; how much 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 I 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 wus 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 he bad ten cents. The other says, 4 fifths of your money 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. 7 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? |