92. 2000 soldiers, having lost 105 barrels of bread, weighing 200 lb. each, were obliged to subsist on 12oz. a day for 12 weeks. Had none been lost, they might have have had 14 ounces a day, the same time. What was the whole weight including what was lost, and how much had they left to subsist on?

Ans.

SThe whole weight, 147000 lb. {Left to subsist on, 126000 93. 2000 soldiers (after losing one seventh part of their bread) had each 12 ounces a day for 12 weeks. What was the whole weight of their bread including that lost, and also the weight lost; and how much might they have had per day each man, if none had been lost?

Ans.

The weight was 147000 lb.

The loss, 21000.

Had none been lost they might have had 14 oz. per day.

94. If one degree of a great circle of the earth be 694 English statute miles, how many statute miles is the circumference of the earth, it being 360 degrees?

Ans. 25020 miles.

95. If the circumference of the earth be 25020 English statute miles, and 69 such miles make one degree, how many degrees is it? Ans. 360. 96. If 25020 English statute miles make 360 degrees, how many such miles make one degree?

Ans. 694. 97. If 25020 English statute miles make 360 degrees, how many degrees will 69 such miles make?

Ans. 1.

98. Shipped for the West Indies, 2000 barrels of beef, which cost me $10,50, per barrel, paid cooperage $20,37, truckage $100, wharfage $80: I demand how much the beef cost per barrel when on board.

Ans.

S$10,60,0,185. Or 10 dollars 60 cents, no mills, 185 thousandths of a mill. Here follow a few examples to exercise the pupil in decimals...

1. If,9 of a pound of coffee cost,15 of a pound, how much will 253,7 lb. cost?

2534

Ans. £0,1499, or £0,15 nearly.

3. If,25 of a gallon of wine cost,8 of a dollar, what will,85 of a gallon cost? Ans. $2,72, 4. If,85 of a gallon of wine cost $2,72, how much will ,25 of a gallon cost? Ans. $0,80, i. e. ,8 of a dollar.

NOTE. The third and fourth examples exactly prove each other, though sometimes the answer in one, not being perfect, will not prove by varying their order.

5. If tea be sold for 73,4 cents per pound, how much will 61,3 pounds cost? Ans. $44,99,42.

6. If 61,3 pounds of tea cost $44,9942, what is the price per pound? Ans. 73,4 cents. 7. If 2,5 pounds of tobacco cost,75 of a dollar, how much will 18,5 cost?

Ans. $5,55.

8. If 18,5 pounds of chocolate cost $5,55, how much will 2,5 pounds. cost? Ans. ,75 cents.

$2,39 per hogshead ?

9. What is the value of,15 of a hogshead of lime, at Ans. 35,85 cents. 10. If,15 of a hogshead of lime cost 35,85 cents, what is it per hogshead? Ans. $2,39. 11. If ,75 of a ton of hay cost $15, what is it per Ans: 20 dolls.

ton ?

12. If a barrel of rum cost 20 dolls. what is ,75 of a barrel worth? Ans. 15 dolls. 13. Three men at a tavern, had run up a score, which they (being ignorant in numbers) proposed to pay as follows; A to pay,25, B,5 and C,75, to which the host agreed. Did he gain or lose by this mode of payment, and how much? Ans. he gained 5 of the bill.

SINGLE RULE OF THREE INVERSE.

Inverse Proportion is known by more requiring less, or less requiring more; after stating the terms as directed in Direct Proportion.

Multiply the first and second terms together, and divide the product by the third, the quotient will be the fourth term or answer.

The proof of examples in this, is the same as in Direct Proportion.

NOTE. If there are several denominations in any, or all the terms, they must be reduced to the lowest, as directed in Direct Proportion.

EXAMPLES.

4. If 100 dolls. in 12 months gain 6 dolls. interest, what principal will gain the same in 8 months?

mo. g mo.

12: 100 :: 8
12

8)1200

$150 Ans.

2. If 150 dolls. in 8 months, gain 6 dolls. interest, what principal will gain the same in 12 months?

8: 150 :: 12

8

12)1200

dolls. 100 Ans.

3. If 150 dolls. in 8 months gain 6 dolls. interest, in what time will 100 dolls. gain the same ?

1508: 100

8

100)12/00

12 months, Ans.

4. If 100 dolls. in 12 months ga in time will 150 dolls. gain the same ?

12

100: 12:: 150

dolls. in what

5. If 7 men can do a piece of work in 10 days, how many men can do the same in 5 days?

Ans. 14.

6. If 14 men can do a piece of work in 5 days; how many men can do the same in 10 days?

Ans. 7.

7. If a man perform a journey in 15 days, when the days were 12 hours long, how long ought the days to be, to travel the same distance in 12 days? Ans. 15 hours.

8. If a man perform a journey in 12 days, when the days were 15 hours long, another man travelling at the same rate, is 15 days going the same distance, how long were the days when the second man travelled?

9. A farmer hired a man for a year, a coat worth 15 dolis. and 120 dolls. they parted; the farmer gave him $52,50, how long did he tarry?

Ans. 12 hours. was to give him but disagreeing, besides the coat,

Ans. 6 months.

10. A man has a garment making, which takes 2 yards of cloth of 1 yard wide; as he wishes it to be lined with shalloon of of a yard wide, how much will complete the lining? Ans. 4 yards.

11. If 48 men can build a wall in 24 days, how many men can do the same in 192 days ? Ans. 6 men.

12. If I lend my friend 100 dolls. for 6 months, (allowing 30 days to a month) how long ought he to lend me 1000 dols. to requite my kindness? Ans. 18 days.

13. How many yards of matting, that is half a yard wide, will cover a room that is 30 feet long, and 18 wide? Ans. 120 yds.

L

14. How much in length, that is 3 inches wide, will make a square foot ?

Ans, 4 feet.

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THE RULE OF PROPORTION;

Or,

THE RULE OF THREE, STATED BY A METHOD WHICH RENDERS ALL DISTINCTIONS OF DIRECT, INVERSE, SINGLE, OR double proPORTION, UNNECESSARY.

CASE I. When three numbers or terms only are given.

RULE. Write down that number or term which is of the same kind or quality, the answer is to be, for the middle term, and reduce it to its lowest denomination.

2. Consider whether by the nature of the question, the answer must be more than the middle term, if so set down the greater of the other two numbers at the right of the middle term, and the less at the left; but if the answer must be less than the middle term, set the less number at the right, and the greater at the left.

3. Multiply the middle and right hand terms into each other for a dividend, which divide by the left hand term, the quotient will be the answer in the same denomination the middle term was reduced to, which may (if need be) be reduced to its proper terms.

NOTE. If any or all the terms be of several denomina, tions, they must be reduced as in the Rule of Three Direct, c.

Questions in this rule may be proved by varying their order.

EXAMPLES.

1. If 28s. will pay for the carriage of 1 cwt. 150 miles, how far can 6cwt. be carried for the same money?

6 150 1

I

6)150

Ans. 25 miles.