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42 But 5 : 2 :: 22 (the whole number of eggs) :
5' 4x Whence = the price of both sorts, when mixed
5 together at the rate of 5 for 2d.,
1 1 42 And consequently it
=4, by the question,
5 That is 15x+10x—24x=120, or x=120, the number of eggs of each sort, as required.
9. If A can perform a piece of work in 10 days, and B in 13; in what time will they finish it, if they are both set about it together ?
Let the time sought be denoted by x,
23 10. 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 both of them together produce the same effect ?
Let the time sought be denoted by x, Then a : e::*:: = part of the effect produced
=e (the whole effect) by the question, Or-+
=1 by dividing each side by e,
11. How much rye at 4s. 6d. a bushel, must be mixed with 50 bushels of wheat, at 68. a bushel, so that the mixture may be worth 5s. a bushel ?
Letx=the number of bushels required, Then 9x is the price of the rye in sixpences, And 600 the price of the wheat in ditto, Also (50+x) X10 the price of the mixture in ditto, Whence 9x+600=2500+10x, by the question, Or, by transposition, 10x -9r=600-500, Consequently r=100 the number of bushels required.
12. A labourer engaged to serve for 40 days, on condition that for every day he worked he should receive 20d., but for every day he was absent he should forfeit 8d., : now at the end of the time, he had to receive 11. 11s. 8d. ; how many days did he work, and how many was he idle ?
Let the number of days that he worked be denoted by x,
Then will 404, be the number of days he was idle, Also 20x the sum earned, and (40-x)X8.
Or 320 - 8x the sum forfeited, Whence 20x—(320 - 8x) = 380d.(= 1l. 11s. 8d.), by the question,
That is 20x320+8x3380,
Consequently x = = 25, the number of days he
worked, and 40-x=40-25=15, the number of days he was idle.
QUESTIONS FOR PRACTICE.
many had he?
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 61 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 ?
Ans. 178. 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
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 ?
Aps. 24 feet
1 5. After paying away of my money, and then of the
5 remainder, I had 72 guineas left; what had I at first ?
Ans. 120 guineas 6. It is required to divide 3001 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 1001., B 501., c 1501. 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 40 ?
Ans. 65 9. At a certain election, 1296 persons voted, and the successful candidate had a majority of 120; how many voted for each ?
Ans. 708 for one, and 588 for the other
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, À and B, lay out equal sums of money in trade ; A gains 1261, and B loses 871., and A's money is now double of B’s ; what did each lay out?
Ans. 3001. 12. A person bought a chaise, horse, and harness, for 601. ; the horse came to twice the price of the harness,
; and the chaise to twice the price of the horse and harness; what did he give for each ?
Ans. 131. 6s. 8d for the horse, 61. 13s. 4d.
for the harness, and 401. for the chaise 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 31. a year, and a livery, but was turned away at the end of seven months, and received only 21. 138. 4d. and his li. very ; what was its value ?
Ans. 41. 16s. 15. A person left 5601. 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 4001., daughter 1601. 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 ?
Ans. 24 17. Two persons, A and B, have both the same income; A saves a fifth of his yearly, but B, by spending 501 per annum more than A, at the end of four years, finds himself 100l. in debt; what was their income?
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 shil. ling apiece more to pay ; required the number of persons, and the quota of each ?
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 15. ; 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 ?
Ans. 114d. 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, i of the whole plus 25 gallons was spirits, and } part minus 5 gal. lons was water ; how many gallons were there of each?
Ans. 85 of wine, and 35 of water 22. A bill of 1201. 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 278. ?
Aps. 50 23 Two travellers set out at the same time from Lon. don and York, whose distance is 197 miles ; one of them goes 14 miles a day, apd the other 16 ; in what time will they meet?
Ans. 6 days 133 hours. 24. There is a fish whose tail weighs 91b., 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?
Aas, 721b. 25. It is required to divide the number 10 into three