In the same manner, if he sold x oranges at 5 cents apiece, then he sold 20 - oranges at 4 cents apiece. 5 cents apiece would come to 5 x cents, and 20 – 4 cents apiece would come to 4 times 20 x cents, which is 80-4 cents. x oranges at - oranges at These added together must make 90 cents, therefore 5x+80–4= = 90 By transposing 80 and uniting terms, x = 10 at 5 cents. 23. A man dying left an estate of $2500 to be divided between his two sons, in such a manner, that twice the elder son's share should be equal to three times the share of the second. Required the share of each. Let x denote the younger son's share. Then 2500-x will denote the elder son's share. Twice the elder son's share is 5000 - 2 x. By transposition, 5 x 5000 x = 1000 2500-1000 = 1500 Ans. Elder son $1500, younger son $1000. 24. Two robbers, after plundering a house, found they had 35 guineas between them; and that if one of them had 4 guineas more, he would have twice as many as the other. How many had each ? 25. A man sold 45 barrels of flour for $279; some at $5 and some at $8 per barrel. How many barrels were there of each sort ? 26. A man sold some oxen and some cows for $330; the whole number was 15. He sold the cows for $17 apiece, and the oxen for $32 apiece. How many were there of each sort? 27. After A had lost 10 guineas to B, he wanted only 8 guineas in order to have as much money as B; and together they had 60 guineas. What money had each at first? Let x be the number of guineas A had. Then 60 will be the number B had. A lost 10 to B, therefore A's is diminished by 10, and B's increased by 10, which makes A's x - 10, and B's 70 — x. By the conditions, x-10+8=70-x Transposing and uniting, 2x=-72 60-36 = x36 what A had. = 28. Divide the number 197 into two such parts, that four times the greater may exceed five times the less by 50. 29. Two workmen were employed together for 50 days, at 5 shillings per day each. A spent 6 pence a day less than B did, and at the end of the 50 days he found he had saved twice as much as B, and the expense for two days over. What did each spend per day? Let a denote what A spent per day (in pence). x Then 60x (5s. being 60d.) will be what he saved per day. B saved 6d. less than A. Therefore 54 x will be what B saved per day. Multiplying both by 50, the number of days, A saved 3000-50 x, and B saved 2700-50 x. By the conditions A saved 2 x more than twice what B saved. Therefore 3000 50 x 5400 Transposing and uniting, 48 x = 2400 x = 50 50+ 6 = 56 100x + 2 x V. 1. Two persons talking of their ages, A said he was 25 years older than B, and that one half of his age was equal to three times that of B wanting 35 years. of each? What was the age 3x-35= x+25 2 6x70= x + 25 6x X= =25+ 70 5 – 95 x=19= =B's age. x+25=44 A's age. Note. Since of x+25 is 3x 3x-35. 35, x+25 must be twice 2. Two men talking of their horses, A says to B, my horse is worth $25 more than yours, and of the value of my horse is equal to of the value of yours. What is the value of each ? Let a denote the value of B's horse. Then the value of A's will be x +25. } of x+25 is *+25 is 3 times as much, that is 3x-3x+75 5 5 By the conditions, 4 Multiplying by 5, 4 Multiplying by 4, 15 x = 12 x + 300 15x=3x+75 3x+75 5 x=100 Ans. A's $125, B's $100. Proof. The first condition is evidently answered. With regard to the second, of 125 is 75, and of 100 is 75. 924 3. Two men talking of their ages, one says, my age is now of yours, but in twenty years from this time, if we live, it will be of yours. Required the age of each. Suppose the age of the elder x. Then the younger will be 3x 4 In 20 years the age of the elder will be x + 20, and of the Multiplying by 4, 16x + 320 = 15x+400 Transposing 15x, 16x-15x-400-320 and 320, x= 80 age of elder. 3x = 60 age of younger. 4. A man being asked the value of his horse and chaise, answered, that the chaise was worth $50 more than the horse, and that one half of the value of the horse was equal to one third of the value of the chaise. Required the value of each. 5. Two persons talking of their ages, the first says, of my age is equal to of yours; and the difference of our ages is 10 years. What are their ages? 3 6. There are two towns situated at unequal distances from Boston, and on the same road. They are 30 miles apart. of the distance of the second from Boston is equal to of the distance of the first. What is the distance of each from Boston? 7. A man being asked the value of his horse and saddle, answered, that his horse was worth $114 more than his saddle, and that of the value of his horse was 7 times the value of What was the value of each? his saddle. 8. A hare is 40 rods before a greyhound, but she can run only as fast as the greyhound. How far will each of them run before the greyhound will overtake the hare? 9. A gentleman paid 4 labourers $136; to the first he paid 3 times as much as to the second wanting $4; to the third one half as much as the first, and $6 more; and to the fourth 4 times as much as to the third, and $5 more. How much did he pay to each ? 10. A man bought some cider at $4 per barrel, and some beer at $7. There were 6 barrels more of the cider than of the beer; and of the price of the beer was equal to of the price of the cider. Required the number of barrels of each. 11. Two men commenced trade together; the first put in £40 more than the second, and the stock of the first was to that of the second as 14 to 5. What was the stock of each ? 14 to 5 signifies the second is of the first. 12. A man's age when he was married was to that of his wife as 3 to 2; and when they had lived together 4 years, his age was to hers as 7 to 5. What were their ages when they were married? 13. A and B began trade with equal sums of money. In the first year A gained £40, and B lost £40; but in the second, A lost one third of what he then had, and B gained a sum less by £40 than twice the sum A had lost; when it appeared that B had twice as much money as A. What money did each begin with? Let x be the number of pounds each had at first. Then x +40 will be the sum A had at the end of the first year; and 2 40 the sum B had. The second year A lost of what he then had, consequently he saved; his sum will then be 2 x + 80 3 B gained twice as much as A lost wanting £40; his will be' 4x+1603x-120+2x+80-120. Note. In this example the result had the sign-in both members, but by transposing it has the sign +. It would have been the same thing if the signs had been changed without transposing. The result would have come out right if the first member had been made the second, and the second first, in the first equation. 14. A person playing at cards, cut the pack in such a manner, that of what he cut off were equal to of the remainder. How many did he cut off? 15. Divide $183 between two men, so that of what the first receives, shall be equal to of what the second receives. What will be the share of each? 16. A man sold 20 bushels of grain, rye and wheat; the rye at 5s. and the wheat at 7s. per bushel; of the rye came to as much as of the wheat. How much was there of each? 17. What number is that from which if 5 be subtracted two thirds of the remainder will be 40? 18. A man has a lease for 99 years; and being asked how |