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3 What sum is that, of which the }, { and make 74.

answer 1201. 4. What sum of money, at 6 per cent. per annum, simple interest, will amount to 5001. in 10 years ? answer 3121 10s.

5 Three unequal vents will severally empty a vessel of 120 gallons in 1 hour, 2 hours, and 3 hours; if running together, what time is necessary? answer 32min. 4311 sec.

6 Of a certain' sum given A, B1, Bd, and D the rest, which is 281. the sum is required ?

answer 1121. 7 What is the age of a person who says, that if of the years I have livedbe multiplied by 7, and of them be added to the product, the sum will be 292? answer 60 years. 8 Required the sum, the f, 1, and of which made 941.

answer, 1201. at 6 per cent.

per annum, will amount to 8601. in 12 years ?

answer 5001. 10 A person having about him a certain number of dollars, said, that , }, { and of them would make 57 ; how many had he?

answer 60. 11. A schoolmaster being asked how many scholars he had, answered, if to double the number I add , , and of them, I shall have 333; how

many

had he? ansuer 108 12 A saves į of his income; but B who has the same salary, by living twice as fast as A, sinks 501. a year; how much then have they per annum?

answer 1501, each. 13 The yearly interest of Charlotte's money, at 6 per cent. exceeds zo of the principal by an 1001. and she does not intend to marry any man, who is not scholar enough to tell her fortune; pray what is it?

answer 100001.

9 What sum,

DOUBLE Position.

Double position teaches to solve such questions as require two supposed numbers in the operation.

RULE. Suppose two numbers, and work with each agreeably to the tenor of the question, noting the errors of the results: multiply the errors of each operation into the supposed number of the other; then,

If the errors be alike, i. e. both too much, or too little, take their difference for a divisor, and the difference of the product for a dividend : but if unlike, take their sum for a divisor, and the sum of the products for a dividend. Note. In many instances, if o be used for the first, and 1 for the second of

the supposed number, the first of the errors, divided by their difference, will be the answer. Proof as in single position.

EXAMPLES. 1 A farmer hired a labourer on this condition, that for every day he worked, he should receive 12d. but for every day he was idle he should be fined 8d. when 390 days were past, neither of them was indebted to the other ; how inany days did he work.

Suppose ist. 140 working days, * 2d. 150
390_140=250 idle

240

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2 Divide 1001. so that B may have twice as much as A, wanting 8l. and C three times as much, wanting 151. what is each man's share ?

answer A 202 10s. B 381. C 461 108. 3 Of 100l. expenditures, B paid 101. more than A, and C as much as A and B; éach man's part is required ?

answer A 201. B 301. C 501. 4 A is 20 years of age : B's age is A's and half C's, and C's equals them both; their several ages are required ?

answer A 20, B 60, C 80 years. 5 The head of a fish is 9 inches long, and its tail is as long as its head and half the body, and the length of the body equal those of the head and tail, what is its whole length?

answer 6 feet. 6 A labourer hired for 40 days upon this condition, that he should receive 20d. for every day he wrought, and forfeit 10d, for every day he was idle; at settlement' he received 21 1s 8d. how many days did he work, and how many was he idle ?

answer wrought 30 days, idle 10. 7 Bought 15 yards for 31 10s. viz. damask at 8s. per yard, and lining for it, at 3s. per yard; what quantity was there of each ?

S 5 yards damnask.

10 ditto lining. 8 A and B put equal sums of money in trade; A gained a sum equal to of his stock, and B lost 225l. then A's inoney was double that of B's; what capital did each of them begin with ?

answer 6001. 9 When first the marriage knot was ty'd

Between my wife and me,
My age was to that of my bride

As three times three to three ;
But now when ten, and half ten years,

We man and wife have been,
Her age to mine exactly bears,

As eight is to sixteen:
Now tell, I pray, from what I've said,
What were our ages when we wed?

$ Thy age when marry'd must have been

answer

answer

PERMUTATION.

PERMUTATION. ERMUTATION is a rule for finding how many

varied in positions, or succession ; thus, abc, acb, bac, bca, cab, cba, are six different positions of three letters.

RULE. Multiply all the terms of the natural series continually from 1 to the given number inclusive, the last product will be the changes required.

EXAMPLES. 1 In how many different positions can 5 persons place themselves at a table ? 1x2x3 X4 X5=120 answer.

2 What number of changes may be rung upon 12 bells, and in what time may they be rung, allowing 3 seconds to

$ 479001600 changes. 3 What time will it require for 8 persons to seat them-selves every day differently at dinner? ans. 110yr. 142da.

4 What number of variations will the 26 letters of the alphabet admit of? ans. 403291461126605635584000000

every round:

answer

{is hours.

COMBINATION.

different

ways a less number of things may be combined out of a greater; thus, out of the letters a, b, c, are three different combinations of two, viz. ab, ac, bc.

RULE. Take a series proceeding from and increasing by a unit, up to the number to be combined ; and another series of as many places, decreasing by unity, from the number out of which the combinations are to be made ; multiply the first continually for a divisor, and the latter for a dividend, the quotient will be the answer.

EXAMPLES. | How many combinations of 5 letters in 10?

치 2 Løx9x8x7x6 =252 answer.

1x3X3XAXS

2

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