But 5 2 2x (the whole number of eggs) : 4x 5 price of both sorts together, at 5 for 2d. Or 3x+2x Or 15x+10x-24x=120; Whence x120= number of eggs of each sort required. 10. A can do a piece of work alone in ten days, and B in thirteen; if both be set about it together, in what time will it be finished? Let the time sought be denoted by x, 13% That is, +x=13, or 13x+10x=130; IO And therefore 23x=130, or x=35 days, the time required. 11. If one agent A alone can produce an effect e in the time a, and another agent B alone in the time b; in what time will they both together produce the same effect? Let the time sought be denoted by x. ex Then a part of the effect produced by A, : e ::x: 1. What two numbers are those, whose difference is 7, and sum 33 ? Ans. 13 and 20. 2. To divide the number 75 into two such parts, that three times the greater may exceed seven times the less by Ans. 54 and 21. 15. I 3. In a mixture of wine and cider, of the whole plus 25 gallons was wine, part minus 5 gallons was cider; how many gallons were there of each? Ans. 85 of wine and 35 of cider. 4. A 4. A bill of 120l. was paid in guineas and moidores, and the number of pieces of both sorts used was just 100; how many were there of each ? Ans. 50 of each. 5. Two travellers set out at the same time from London and York, whose distance is 150 miles; one of them goes 8 miles a day, and the other 7; in what time will they ineet? Ans. 10 days. 6. At a certain election 375 persons voted, and the candidate chosen had a majority of 91; how many voted for each ? Ans. 233 for one and 142 for the other. 7. There is a fish, whose tail weighs 9lb. his head weighs as much as his tail and half his body, and his body weighs as much as his head and his tail; what is the whole weight of the fish? Ans. 72lb. 8. What number is that, from which if 5 be subtracted, of the remainder will be 40? Ans. 65. 9. A post is one fourth in the mud, one third in the water, and 10 feet above the water; what is its whole length? Ans. 24 feet. 10. After paying away one fourth and one fifth of my money, I found 66 guineas left in my bag; it at first? what was in Ans. 120 guineas. II. A's age is double that of B, and B's is triple that of C, and the sum of all their ages is 140; what is the age of each? Ans. A's 84, B's 42 and C's 14. 12. Two persons, A and B, lay out equal sums of money in trade; A gains 1261. and B loses 871. and A's money is now double that of B; what did each lay out? Ans. 300l. 13. A person bought a chaise, horse and harness, for Gol.; the horse came to twice the price of the harness, and and the chaise to twice the price of the horse and the harness; what did he give for each? Ans. 131. 6s. 8d. for the horse, 61. 13s. 4d. for the har ness, and 401. for the chaise. 14. Two persons, A and B, have both the same income; A saves one fifth of his yearly, but B, by spending 50l. per annum more than A, at the end of 4 years finds himself rool. in debt; what is their income? Ans. 1251. 15. A gentleman has two horses, and a saddle worth gol. Now if the saddle be put on the back of the first horse, it will make his value double that of the second; but if it be put on the back of the second, it will make his value triple that of the first; what is the value of each horse? Ans. One 30l. and the other 401. 16. To divide the number 36 into three such parts, that of the first, of the second, and of the third, may be all equal to each other. Ans. The parts are 8, 12 and 16. 17. A footman agreed to serve his master for 81. a year and a livery, but was turned away at the end of 7 months, and received only 2l. 13s. 4d. and his livery; what was its value? Ans. 41. 16s 18. A gentleman was desirous of giving 3d. a piece to some poor beggars, but found, that he had not money enough in his pocket by 8d.; he therefore gave them each 2d. and had then 3d. remaining; required the number of beggars. Ans. II. 19. A hare is 50 leaps before a grey hound, and takes 4 leaps to the grey hound's 3; but 2 of the grey hound's leaps are as much as 3 of the hare's; how many leaps must the hound take to catch the hare? Ans. 300. grey 20. A person at play lost 3 shillings; after which he W w of his money, and then won lost of what he then had, and and then won 2 shillings; lastly, he lost then had, and, this done, found he had but ing; what had he at first? of what he 12s. remainAns. 20s. 21. To divide the number 90 into 4 such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, the sum, difference, product, and quotient, shall be all equal to each other. Ans. The parts are 18, 22, 10, and 40, respectively. 22. The hour and minute hands of a clock are exactly together at 12 o'clock; when are they next together? Ans. 1 hour, 5 min. 23. There is an island 73 miles in circumference, and 3 footmen all start together to travel the same way about it; A goes 5 miles a day, B 8,, and C 10; when will they all come together again? Ans. 73 days. 24. If A can do a piece of work alone in 10 days, and A and B together in 7 days, in what time can B do it alone? Ans. 23 days. 25. If three agents, A, B and C, can produce the effects a, b, c, in the times e, f, g, respectively; in what time would they jointly produce the effect d? 26. If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days; how many days will it take each person to perform the same work alone? Ans. A 1434 days, B 1743, and C 23377 QUADRATIC EQUATIONS. A SIMPLE QUADRATIC EQUATION is that, which involves the square of the unknown quantity only. An |