found by dividing the known quantity by the coefficient of the un-. known quantity. 10. A man bought some oranges, some lemons, and some pears, for 156 cents ; the oranges at 6 cents each, the lemons at 4 cents, and the pears at 3 cents; there was an equal number of each sort. Required the number of each. 11. In fencing the side of a field, the length of which was 450 yards, two workmen were employed; one fenced 9 yards, and the other 6 yards per day. How many days did they work? 12. Three men built 780 rods of fence; the first built 9 rods per day, the second 7, and the third 5; the second worked three times as many days as the first, and the third, twice as many days as the second. How many days did each work? 13. A man bought some oxen, some cows, and some calves for $348; the oxen at $38 each, the cows at $18, and the calves at $4. There were three times as many cows as oxen, and twice as many calves as cows. How many were there of each sort? 14. A merchant bought a quantity of flour for $132; for one half of it he gave $5 per barrel, and for the other half $7. How many barrels were there in the whole ? Let x denote one half the number of barrels. 15. From two towns, which are 187 miles apart, two travellers set out at the same time with an intention of meeting; one of them travels at the rate of 8, the other of 9 miles each day. In how many days will they meet? II. 1. A cask of wine was sold for $45, which was only of what it cost. Required the cost. is the same as of 3x. Now if of 3 x is 45, 3x itself must be 4 times 45, or 180; 3 x being 180, x must be of 180, which is 60. 2. A man, being asked his age, answered, that if its half and its third were added to it the sum would be 88. What was his age? Let x denote his age; then, of 11 x being 88, 11 x will be 6 times 88, 11 x = 528 Dividing by 11, x=48 3. If of a hogshead of wine cost $65; what will a hogshead cost at that rate? and under water, and 5 feet out of 4. There is a pole water; what is the length of the pole? Let x denote the whole length. Then equal to the whole length. Hence, Reducing to a common denominator, Since the two members are equal, if 5 be subtracted from both, they will still be equal; hence, 6 5 6 Proof. One half of 30 is 15, and one third of thirty is 10. Now 30 15+ 10 + 5. There is another mode of reducing the above equation which in most cases is to be preferred. is the same in principle. If both members of an equation be multiplied by the same number, they evidently will still be equal. In the equation, First multiply both members by 2, the denominator of one of the fractions, and it becomes, Next multiply both members by 3, the denominator of the other fraction, and it becomes, 6x=3x+2x+30 or 6x=5x+30. Subtracting 5 x from both members, x30 as before. of 5. In an orchard of fruit trees of them bear apples, them pears, of them plums, 7 bear peaches, and 3 bear cherries; these are all the trees in the orchard. How many are there? 6. A farmer, being asked how many sheep he had, answered, he had them in four pastures; in the first he had of them, in the second, in the third, and in the fourth he had 24 sheep. How many had he in the whole? 7. A person having spent and of his money, had $263 left. How much money had he at first? 8. A man driving his geese to market, was met by another, who said good morrow, master, with your hundred geese; said he, 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? 12 9. A and B having found a bag of money, disputed about the division of it. A said that and and of the money made $130, and if B could tell how much money there was, he should have it all, otherwise none of it. How much money was there in the bag? 10. Upon measuring the corn produced in a field, being 96 bushels, it appeared that it had yielded only one third part more than was sown. How much was sown? / 11. A man sold 96 , and to the second loads of hay to two persons; to the first of what his stack contained. How ma ny loads did the stack contain at first? 12. A and B talking of their ages, A says to B if,, and of my age be added to my age, and 2 years more, the sum will be twice my age. What was his age? 4 13. What sum of money is that whose 1, 1, and part added together amount to £9 ? 14. The account of a certain school is as follows: of the boys learn geometry, learn grammar, learn spelling, and 9 learn to read. 20 of scholars in the school? learn arithmetic, What is the number 15. There is a fish whose head weighs 9 lb. his tail weighs as much as his head and half his body, and his body weighs as much as his head and tail both. What is the weight of the fish? Represent the weight of the body by x. 16. There is a fish whose head is 4 inches long, the tail is twice the length of the head, added to of the length of the body, and the body is as long as the head and tail both. What is the whole length of the fish? 17. A and B talking of their ages, A says to B, your age is twice and three fifths of my age, and the sum of our ages is 54. What is the age of each? 18. A man divided $40 between two persons; to the first he gave a certain sum, and to the second only as much. How much did he give to each? ་ Let a denote the share of the first, 3 will 3x will denote the share 5 of the second. These added together must make $40. 19. Three persons are to share $290 in the following manner: the second is to have two thirds, and the third three fourths as much as the first. What is the share of each? 20. A farmer wishes to mix 100 bushels of provender, consisting of rye, barley, and oats, so that it may contain as much barley as oats, and as much rye as barley. How much of each must there be in the mixture? 21. Divide 40 apples between two boys in the proportion of 3 to 2. The proportion 3 to 2 signifies that the second will have as many as the first. 22. A gentleman gave to 3 persons £98. The second received five-eighths of the sum given to the first, and the third one-fifth of what the second had. What did each receive? 23. A prize of $1280 was divided between two persons, in the proportion of 9 to 7. What was the share of each ? 24. Three men trading in company, put in money in the following proportion; the first 3 dollars as often as the second 7, and the third 5. They gain $960. What is each man's share of the gain? Observe, the second put in 3 of what the first put in, and the third put in §. 25. Three men traded together; the first put in $700, the second $450, and the third $950. They gained $420. What was the share of each ? Observe, the second put in 48=4 put in, &c. of what the first |