18 How many yards of matting, that is half a yard wide, will cover a room that is 18 feet wide and 30 long?

answer 120 yards. 19 How wide must a lot of ground be to contain an acre, when it is 13 poles in length?

answer 11P. 4yds. 2ft. oin. 2b.c. 20 If, when the price of a bushel of wheat is 6s 3d. the penny loaf weighs 90%. what ought it to weigh, when wheat is at 8s zd. per bushel? answer 6oz. 13dr. 21 In what time will 600l. gain 50l. interest, when 80% would gain it in 15 years?

Application.

If 3 quarters of a yard of velvet cost yards can I buy for 13/ 15s 6d.?

answer 2 years

73 3d how many answer 28yds. 2qr.

2 If an ingot of gold weighing 9lb. 9oz. 12dwt. be worth 4114 125. what is that per grain?

answer id.2 3 A borrowed of B 250l. for 7 months; and in retur lends him 300l. how long ought B to keep it, that the interest of it may be equal to that of the first sum ?

answer 5mo. 25da 4 If a person's income be 500 guineas a year, and he spend 19s 7d sterling per day; how much will he have saved at the year's end? answer 1671 125 Id. sterling5 At 135 2d per yard, what is the value of a piece of cloth containing 52 English ells and 3yrs.?

answer 431 8s 5d. 6 If 30 men can perform a piece of work in 11 days; how many men will accomplish another piece of work, four times as large, in 12 days?

answer IIO men.

7 The rents of a whole parish amount to 1750l. on which is assessed 32/ 16s 3d. what is that in the pound?

answer 4d1⁄2 8 Bought three tons of oil for 151 145. 85 gallons of which being damaged, I desire to know how I may sell the remainder per gallon, so as neither to gain nor lose thereby ? answer 4s 6d. 9 If the carriage of 5C. 14lb. for 96 miles, be 32s. 6d. how far may I have 3C. 1gr. carried for the same money? answer 151 M. 3fur. 3P. 10 Bought 200 yards of cambric for 90l. which being damaged, am willing to lose 7 10s by the whole, at what rate then must it sell per ell English?

answer 100 ad.3

?

11 If, for 48. 225C. be carried 512 miles, how many hundred weight may be carried 64 miles for the same money answer 1800G.

12 Bought a parcel of cloth, at the rate of 6s 6d. for every two yards, of which a certain quantity was sold at the rate of 18s 9d. for every five yards, and gained thereby as much as 180 yards cost; how many yards were sold?

answer 1170 yards. 13 A certain steeple projected upon level ground a shadow to the distance of 633 ft. 4in. when a staff 3 feet in length, perpendicularly erected, cast a shadow 6ft. 4in. from Irence the height of the steeple is required?

answer 100 yards. 14 If 12 yards of yard wide stuff exactly line 8 yards of silk of another breadth; how many yards of the latter will fine 24 pieces of the former, each piece containing 20 yards? answer 320 yards.

15 Laid out 100l. upon serges and shalloons; the value of the shalloons was be. and the quantity of serge 237 yards; also for every two yards of serge there were three of shalloon how many yards of shalloon were there, and what was the value of one yard of each sort?

miles a day; B follows at the rate of 25 miles a day; in what time and what distance will he overtake A?

answer 20 days, and 500 miles. 21 If 58 gallons of water, in one hour, fall into a cistern containing 230 gallons, and by a pipe in the cistern, 35 gallons run out in an hour; in what time will it be filled?

answer 15h. 20min. 22 A certain cistern has four pipes; by the first it will be filled in ro minutes, by the second in 20, by the third in 40, and by the fourth in 80; in what time will all four, running together, fill it? answer 5min. 20sec. 23 Astronomers compute the earth's orbit, or track which it describes round the sun in 365 days 6 hours, to be about 5969cc000 miles; how far then, per minute, must we be carried through the firmament by this wonderful motion?

ansiver 1134+ miles.

24 Isaac Newton, and others, have found, by nice experi. ments, that sound flies at the rate of 1 142 feet per second, and a person in health has about 75 beats of the artery or pulsations in a minute; now the breadth of a river is required, at one side of which A, firing a gun, B, directly opposite at the other, counts six pulsations at his wrist between seeing the flash and hearing the report?

answer 5481ft. or 1 mile 201ft. 25 If the report of a piece of ordinance be heard one minute and three seconds after the flash was observed; the distance is required? answer 13 miles 5 furlongs.

THE DOUBLE RULE OF THREE.

TH

HE Double rule of three is that, wherein five numbers or terms are given, to find a sixth, three of which are a supposition, and two a demand; and is either direct or in

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correspondent terms of the supposition and demand in the same line, and of one denomination ; as in the subsequent' examples. viz.

1 If three men in 4 days eat 5lb. of bread, how much will suffice 6 men for 12 days?

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12d. 2 If 3 men cat 5lb. in 4 days ; in how many days will

4 men consume 30lb.

6m.

576. To know whether the stating be direct or inverse : Consider the upper pair of extremes, and the lower, each separately with the middle term, as a stating of the single rule, and try them as tauglit in that rule: if both lines be direct; the stating is in direct proportion; but of inverse, if either pair of the extremes be so. Thus, the first example above is di. rect, and the second inverse.

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DIRECT PROPORTION.

RULE. Divide the continual product of the two last extremes and middle term by that of the two first, and the quotient will be the sixth term, or answer.

PROOF. By two statings of the single rule of three. Note. If either of the two first terms, or both, will divide, or can be

divided by any of the three laft, or by any other number without rer mainder, the operation may be abbreviated by cancelling them, and using their quotients aliquot parts in their stead.

EX A MPLE S. 1 If three men in four days eat 5lb. of bread; how much will suffice 6 men for 12 days? If 3m. 2 6m.

6m. 2 12d.

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2 Suppose 4 men in 12 days mow 48 acres; how many acres can 8 men mow in 16 days? answer 128 acres. 3 If 12 oxen in 16 days eat 20 acres of grass; how many acres will serve 24 oxen 48 days?

answer 120 acres.

4 If 10 bushels of oats be sufficient for 18 horses 20 days how many bushels will serve 60 horses 36 days, at that rate? answer 60 bushels. 5 If 56lb. of bread be sufficient for 7 men 14 days; how many pound will suffice 21 men 3 days?

answer 36lb. 6 If 8 men have 3/ 4s. for 4 days work; how much ought 48 men to receive for 16 days? -7 If 700 dols. in half a year will be the interest of 400 dols. for 5 years?

raise 14

answer 761 165. dols. interest; what

ans. 8odols. 8 If 112 acres of grass be mowed by 16 men in 7 days; how many acres may 24 men mow in 19 days?

answer 456 acres. 9 If 16 18s. be the wages of 16 men for 8 days; what sum will 32 men earn in 24 days?

answer 1011 8s. 10 If 757. in 9 months amount to 781 7s 6d. at what rate per cent. is the interest computed? answer 61. per cent. 11 Suppose the wages of 6 persons for 21 weeks be 120/ what will be the hire of 14 persons for 46 weeks?

answer 6131 6s 8d. 12 What is the interest of 259/ 135 5d. for 20 weeks, at

5 per cent? answer 41 19s 10d. 13 If 2 men can do 12 rods of ditching in 6 days; how many rods may be done by 8 men in 24 days?

answer 192 rods. 14 If the carriage of 8C.wt. 128 miles cost 6,40; what must be paid for the carriage of 4C.wt. 32 miles? answer 8octs. 15 If 200lb. be carried 40 miles for 40cts. how much must be paid at that rate for the carriage of 20200lb. 60 miles? answer 60,60

16 If the freight of 9 hogsheads of sugar, each weighing 12 hundred weight, for 20 leagues, cost 161. what must be paid for the freight of 50 casks of ditto, each weighing 2 hundred weight, 100 leagues? answer 92/ 11s 10d.

INVERSE