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worked, and 40–2=40–25=15, the number of days he was idle.
QUESTIONS FOR PRACTICE.
1. It is required to divide a line, of 15 inches in length, into two such parts, that one may be three fourths of the other. Ans. 84 and 6;
2. My purse and money together are worth 20s. and the money is worth 7 times as much as the purse, how much is there in it 7 Ans. 17s. 6d.
3. A shepherd, being asked how many sheep he had in his flock, said, if I had as many more, half as many more, and 7 sheep and a half, I should have just 500; how many had he 7 Ans. 197.
4. A post is one fourth of its length in the mud, one third in the water, and 10 feet above the water; what is is its whole length 2 Ans. 24 feet
1 5. After paying away ; of my money, and then 5 of the
remainder, I had 72 guineas left; what had I at first 7 Ans. 120 guineas
6. It is required to divide 300l between A, B, and c, so that A may have twice as much as B, and c as much as A and B together. Ans. A 100l., B 50l., c 150l.
7. A person, at the time he was married, was 3 times as old as his wife; but after they had lived together 15 years, he was only twice as old; what were their ages on their wedding day ? Ans. Bride's age 15, bridegroom’s 45 8. What number is that from which, if 5 be subtracted, two thirds of the remainder will be 407 Ans. 65 9. At a certain election, 1296 persons voted, and the successful candidate had a majority of 120; how many voted for each 7 Ans. 708 for one, and 588 for the other
... self 100l. in debt; what was their income 2
10. A’s age is double of B's, and B's is triple of c's, 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
11. Two persons, A and s, lay out equal sums of money in trade ; A gains 126l. and B loses 871., and A’s money
is now double of B's ; what did each lay out 7
12. A person bought a chaise, horse, and harness, for 60l. ; the horse came to twice the price of the harness, and the chaise to twice the price of the horse and har
13. A person was desirous of giving 3d. apiece to some beggars, but found 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. 11
14. A servant agreed to live with his master for 3!, a year, and a livery, but was turned away at the end of seven months, and received only 2l. 13s. 4d. and his livery ; what was its value * Ans. 4l. 16s.
15. A person left 560l., between his son and daughter, in such a manner, that for every half crown the son should have, the daughter was to have a shilling; what
were their respective shares? Ans. Son 400l., daughter 160l.
16. There is a certain number, consisting of two places of figures, which is equal to four times the sum of its digits ; and if 18 be added to it the digits will be inverted; what is the number 2 ^ Ans. 24
17. Two persons, A and B, have both the same income; A saves a fifth of his yearly, but B, by spending 50l per annum more than A, at the end of four years, finds himAns. 125l.
18. When a company at a tavern came to pay their reckoning, they found, that if there had been three Persons more, they would have had a shilling apiece less to pay, and if there had been two less, they would have had a shilling apiece more to pay; required the number of persons, and the quota of each 7 Ans. 12 persons, quota of each 5s.
19. A person at a tavern borrowed as much money as he had about him, and out of the whole spent 1s. ; he then went to a second tavern, where he also borrowed as much as he had now about him, and out of the whole spent 1s. ; and going on, in this manner, to a third and fourth tavern, he found, after spending his shilling at the latter, that he had nothing left; how much money had he at first 7 Ans. 1.14d.
20. It is required to divide the number 75 into two such parts, that three times the greater shall exceed seven times the less by 15. Ans. 54 and 21
21. In a mixture of British spirits and water, 4 of the whole plus 25 gallons was spirits, and # part minus 5 gallons was water; how many gallons were there of each Ans. 85 of wine, and 35 of water
22. A bill of 120l. was paid in guineas and moideres, and the number of pieces of both sorts that were used were just 100 ; how many were there of each, reckon
ing the guinea at 21s., and the moidore at 27s. ? Ans. 50
23 Two travellers set out at the same time from London and York, whose distance is 197 miles ; one of them goes 14 miles a day, and the other 16; in what time will they meet 7 Ans. 6 days 133 hours.
24. 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, 72ib. ,
25. It is required to divide the number 10 into three
such parts, that, if the first be multiplied by 2, the second by 3, and the third by 4, the three products shall be
26. It is required to divide the number 36 into three
such parts, that 4 the first, 4 of the second, and 4 of the third, shall be all equal to each other,
- Ans. The parts are 8, 12, and 16
* 27. A person has two horses, and a saddle, which, of itself, is worth 50l. ; now, if the saddle be put on the back of the first horse, it will make his value double that of the second, and 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 40l.
"28. If A gives B 5s. of his money, B will have twice as much as the other has left ; and if B gives A 5s. of his money, a will have three times as much as the other has left; how much had each 7 Ans. A 13s. and B 1 1s.
29. What two numbers are those whose difference, sum and product, are to each other as the numbers 2, 3, and 5, respectively 7 Ans. 10 and 2
30. A person in play lost a fourth of his money, and then won back 3s., after which he lost a third of what he now had, and then won back 2s. ; lastly, he lest a seventh of what he then had, and after this found he had but 12s. ramaining; what had he at first 7 Ans. 20s.
31. A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3, but 2 of the greyhound's leaps are as much as 3 of the hare’s how many leaps
must the greyhound take to catch the hare ? Ans. 300
32. It is required to divide the number 90 into four such parts, that if the first part 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.” Ans. The parts are 18, 22, 10, and 40 33. The quotient and remainder of a sum in division are, each, 21 ; and the divisor is 7 less than their sum : what is the number to be divided. Ans. 1950 34. A man and his wife usually drank out a cask of beer in 12 days, but when the man was from home it lasted the woman 30 days; how many days would the man alone be in drinking it? Ans. 20 days 35. A general, ranging his army in the form of a solid square, finds he has 284 men to spare, but increasing the side by one man, he wants 25 to fill up the square ; how many soldiers had he Ans. 24000 36. 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
the same work alone 7 Ans. A 1434 days, B 173%, and c 23#
A QuaDRAtic Equation, as before observed, is that in which the unknown quantity is of two dimensions, or which rises to the second power; and is either simple or
compound. ".. A simple quadratic equation, is that which contains
only the square, or second power, of the unknown quantity, as b aa.” =b, or a:2 = a where z=y a A compound quadratic equation, is that which contains both the first and second power of the unknown quantity; as
b c aza-Hbr=c, or r2-H. zo-3, In which case, it is to be observed, that every equation of this kind, having any real positive root, will fall under one or other of the three following forms :