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Adding 4 to each, they become x + 4, and 3*+4.

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2

The first is now of the second, or the second is of the

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4. A sum of money was divided between two persons, A and B, so that the share of A was to that of B as 5 to 3. Now A's share exceeded of the whole sum by $50. What was the share of each person?

Let

x= A's share.

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5. The joint stock of two partners, whose particular shares differed by 48 dollars, was to the lesser as 14 to 5. Required the shares.

6. Four men bought an ox for $43, and agreed that those, who had the hind quarters, should pay cent per pound more than those, who had the fore quarters. A and B had the hind quarters, C and D the fore quarters. A's quarter weighed 158 lb., B's 163 lb., C's 167 lb., and D's 165 lb. What was each per lb., and what did each man pay ?

7. A certain person has two silver cups, and only one cover for both. The first cup weighs 12 oz. If the first cup be covered it weighs twice as much as the other cup, but if the second be covered it weighs three times as much as the first. What is the weight of the cover, and of the second cup?

Let

x= weight of the cover.

Then 12+x= weight of the first cup covered.

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8. Some persons agreed to give 6d. each to a waterman for carrying them from London to Gravesend; but with this condition, that for every other person taken in by the way, three pence should be abated in their joint fare. Now the waterman took in three more than a fourth part of the number of the first passengers, in consideration of which he took of them but 5d. each. How many persons were there at first ?

Let

x = the number of passengers at first.

Then +3= the number taken in, &c.

4

9. Four places are situated in the order of the four letters, A, B, C, D. The distance from A to D is 134 miles, the distance from A to B is to the distance from C to D, as 3 to 2, and one fourth of the distance from A to B, added to half the distance from C to D, is three times the distance from B to C. What are the respective distances?

10. A field of wheat and oats, which contained 20 acres, was put out to a labourer to reap for $20; the wheat at $1.20 and the oats $0.95 per acre. Now the labourer falling ill reaped only the wheat. How much money ought he to receive according to the bargain?

11. Three men, A, B, and C, entered into partnership; A paid in as much as B and one third of C; B paid as much as C and one third of A; and C paid in $10 and one third of A. What did each pay in ?

x the sum A contributed.

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+10+1 =

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12. A gentleman gave in charity £46; a part of it in equal portions to 5 poor men, and the rest in equal portions to 7 poor women. Now the share of a man and a woman together amounted to £8. What was given to the men, and what to the women?

Let

Then

the sum a man received.

8-x the sum a woman received, &c.

=

13. Suppose that for every 10 sheep a farmer kept, he should plough an acre of land, and should be allowed an acre of pasture for every 4 sheep. How many sheep may that person keep who farms 700 acres?

Let x = the whole number of sheep.

The number of acres ploughed will.be of the number of sheep; and the number of acres of the pasture will be of the number of sheep; both these added together must be the whole number of acres, &c.

14. A, B, and C make a joint stock; A puts in $70 more than B, and $90 less than C; and the sum of the shares of A and B is of the sum of the shares of B and C.

cach put in?

Let

the sum that B put in, &c.

What did

15. Divide the number 85 into two such parts that if the greater be increased by 7 and the less be diminished by S, they will be to each other in the proportion of 5 to 2.

16. It is required to divide the number 67 into two such parts that the difference between the greater and 75 may be to the excess of the less over 12 in the proportion of 8 to 3.

17. A man bought 12 lemons and a pound of sugar for 56 cents, afterwards he bought 18 lemons and a pound of sugar at the same rate for 74 cents. What was the price of the sugar, and of a lemon ?

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18. A man bought 5 oranges and 7 lemons for 58 cents; afterwards he bought 13 oranges and 6 lemons at the same rate for 102 cents. What was the price of an orange, and of a lemon ?

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19. A footman, who contracted for $72 a year and a livery suit, was turned away at the end of 7 months, and received only $32 and the livery. What was the value of the livery? and a

20. A landlord let his farm for £10 a year in money certain number of bushels of corn. When corn sold at 10s. a bushel, he received at the rate of 10s. an acre for his land; but when it sold for 13s. 6d. a bushel, he received 13s. an acre How many bushels of corn did he receive ?

Let
Then

10x+200

10

x= the number of bushels.

10x+200 the year's rent in shillings;
=x+20= the number of acres.

27x+400 the year's rent at the second rate in six

pences.

27 x + 400

26

the other, &c.

= the number of acres, which must be equal to

21. A man commenced trade with a certain sum of money, which he improved so well, that at the year's end he found he had doubled his first stock wanting $1000; and so he went on every year doubling the last year's stock wanting $1000; at the end of the third year he found that he had just three times as much money as he commenced with. What was his first stock?

22. A man, having a certain sum of money, went to a tavern, where he borrowed as much money as he then had, and then spent a shilling; with the remainder he went to another tavern, where he borrowed as much as he then had, and then spent a shilling, and so he went to a third and a fourth tavern, borrowing and spending as before; after which he had nothing left. How much money had he at first?

23. It is required to divide the number 60 into two such parts, that one seventh of the one may be equal to one eightn of the other.

24. It is required to divide the number 85 into two such parts that of the one added to of the other may make 60. 33 25. It is required to divide the number 100 into two such parts, that if one third of one part be subtracted from one fourth of the other, the remainder may be 11.

26. It is required to divide the number 48 into two such parts, that one part may be three times as much above 20, as the other wants of 20.

27. A man distributed 20 shillings among 20 people, giving 6 pence apiece to some, and 16 pence apiece to the rest. What number of persons were there of each kind?

28. A man paid £100 with 208 pieces of money, a part guineas at 21s. each, and a part crowns at 5s. each. How many pieces were there of each sort?

29. A countryman had two flocks of sheep, the smaller consisting entirely of ewes, each of which brought him 2 lambs. On counting them he found that the number of lambs was equal to the difference between the two flocks. If all his sheep had been ewes, and brought forth three lambs apiece, his stock would have been 432. Required the number in each flock.

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30. When the price of a bushel of barley wanted but 3d. to be to the price of a bushel of oats as 8 to 5, four bushels of bar ley and 7s. 6d. in money were given for nine bushels of oats. What was the price of a bushel of each?

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x = the price of a bushel of oats in pence.

-3 the price of a bushel of barley, &c.

31. A market-woman bought a certain number of eggs at the rate of 2 for a cent, and as many at 3 for a cent, and sold them out at the rate of 5 for two cents; after which she observed, that she had lost four cents by them. How many eggs of each sort had she?

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