Since 15 francs is equal to $14:10, twice $14.10 would equal twice 15 francs; thrice $14:10 would equal thrice 15 francs, and so for other ratios. Therefore, 15 francs must be repeated as many times as $14:10 is contained times in $34.78; that is, 347833 times. Hence, the number of francs required is

of 15 francs 37 times of 15 francs-37 times 1 franc= 37 francs.

The above method of working questions of the Rule of Three is contained in the following simple

RULE.

Of the three terms which are given, one will always be of the same kind as the answer sought; this will be the third term. Then if, by the nature of the question, the answer is required to be greater than the third term, divide the greater of the two remaining terms by the less, for a ratio; but if the answer is required to be less than the third term, then divide the less of the two remaining terms by the greater, for a ratio. Having obtained the ratio, multiply the third term by it, and it will give the answer in the same denomination as the third term.

NOTE.-Before obtaining the ratio by means of the first two terms, we must reduce them to like denominations.

EXAMPLES.

1. If in 7 weeks there are 49 days, how many days are there in 21 weeks?

In this example, the answer is required to be in days; therefore, we must take 49 days for our third term. And, since in 21 weeks there must be more days than in 7 weeks, we get our ratio by dividing 21 by 7, which

gives; the third term, 49 days, multiplied by this, gives 49 days 2, which, by canceling, becomes 147 days, for our answer.

2. If a person perform a journey in 20 days, by traveling 10 hours each day, how long would it take him to perform the same if he travels 8 hours each day?

In this example, our answer is required to be in days; therefore, we must take 20 days for our third term. And, since it will evidently take more days when he travels 8 hours each day, than it did when he traveled 10 hours each day, we must divide 10 hours by 8 hours, for our ratio, which becomes; 20 days, multiplied by this, gives 20 days ×1o, which, by canceling, becomes 25 days for the answer.

3. If of a pound of sugar cost of a shilling, how much will of a pound cost?

23

In this example, our third term is 23 of a shilling. And, since of a pound is less than 1, we must obtain our ratio by dividing by 11, which gives x; this, multiplied by the third term, 23 of a shilling, will give 23 of a shilling ××1. To reduce this with the least labor, we must resort to the method of canceling. Thus, canceling the 23, which occurs in both numerator and denominator, also 13 of the numerator against a part of the 26 of the denominator, our expression will, by this means, become of a shilling of a shilling.

NOTE. This method of canceling should be used when the nature of the question will admit, since it will always very much simplify the operation.

4. If 3 pounds of coffee cost 21 shillings, how much will 10 pounds cost?

shillings must be our third pounds must cost more than divide by, for the ratio, by the third term,

In this example, 21 term, and, since 10 31= pounds, we must making it ; this, multiplied shillings, will give shillings × after canceling, of a shilling × shillings.

×; this becomes, = shillings = 67

It may happen that the three given quantities are all of one denomination; still it will be found that two of them are of one kind, and the third one of another kind, which is like the answer. As an example: What tax must an income of $6000 pay, provided $100 pays $1.03?

Here the three given quantities are $6000, $100, $103, which are all of the same species, viz., money. Nevertheless, the first and second are incomes, and the third is a tax. So that the ratio must be $6000+ $100 -= 60; therefore the tax sought is 60 times $1.03 =$61.80.

=

100

5. If a tree 38 feet 9 inches in height give a shadow of 49 feet 2 inches, how high is that tree, which, at the same time, casts a shadow of 71 feet 7 inches?

2

In this example, our third term is the height of the first tree, which is 38 feet 9 inches 38 feet feet. Our ratio will be obtained by dividing 71 feet 7 inches= 71 feet feet, by 49 feet 2 inches 49 feet= 225 feet, which becomes 5×5; this, multiplied by the third term, 155 feet, gives 155 feet X 352×285. Canceling 6 of the numerator against a part of the 12 of the denominator; also canceling 5, a factor of 155 of the numerator, against 5, a factor of 295 of the denominator, we get 31 feet × 852×3=2092=5619 feet, for the answer.

472

6. If 16 yards of calico cost 21 shillings, how much can be bought for 323 shillings?

7. Sold a tankard for £5 6s. at the rate of 5 s. 4 d. What was its weight?

per ounce.

Ans. 1 lb. 7 oz. 17 pwt. 12 gr.

8. If 300 men consume 70 barrels of provisions in 10 months, how much will 240 men consume in the same time? Ans. 56 barrels.

9. Gave 72 dollars for 5 barrels of fish. How much will 20 barrels cost at the same rate? Ans. $288. 10. If it take 30 yards of carpeting, which is of a yard wide, to cover a floor, how many yards, which is 1 yards wide, will it take to cover the same floor? Ans. 18 yards.

11. If an individual receive a salary of $700 per year, how much will that be for each day, counting 365 days for a year? Ans $19. 12. If the circumference of a wheel is 17 feet, what distance will it pass over in revolving 13 times? Ans. 233 feet.

13. If it take 21 yards of cloth for 2 pair of pantaloons, and 12 yards for 5 coats, how many yards will it require for 7 coats and 8 pair of pantaloons?

15

Ans. 27 yards. 14. If 19 yards of cloth cost 134 dollars, how many Ans. $954.

dollars will 14 yards cost?

15. If 3 bushels of apples cost 13 shillings, how much will 17 bushels cost? Ans. £3 15 s. 10 d.

16. How much must be paid for 33 cords of wood, at 2 dollars per cord? 21 Ans. $8-$8.4375.

17. If a board 16 feet long and 9 inches wide contain

12 square feet, how long must another board be, which is 8 inches wide, to contain the same number of square feet? Ans. 18 feet. 18. If the freight of 7 hogsheads of molasses for 18 miles is 9 dollars, what must be paid for the freight of 21 hogsheads the same distance? Ans. $27.

19. If of a vessel is worth $1729, how much is the whole vessel worth? Ans. $46103.

20. Lent my friend $300 for six months; afterwards he lent me $400. How long may I keep it to balance the favor? Ans. 4 months. 21. If a piece of land 20 rods long, and 8 rods wide, make one acre, how wide must it be, when it is 50 rods long, to contain the same?

22. If a ship sail 90 miles in 7

hours will it require to sail 60 miles?

Ans. 3 rods.

hours, how many

Ans. 4 hours.

23. If of an acre of land is worth 54 dollars, what

is of an acre worth?

24. If I pay of a dollar for sawing

wood, how much must I pay for sawing 5

Ans. $7.20.

one cord of cords? Ans. $4.

25. If 16 yards of cloth are worth of of 201 dollars, what is that per yard?

396

Ans. $3. 26. A man is $1700 in debt, and his estate amounts to but $870. How much can he pay on a dollar?

Ans. $0.51.

27. How many yards of paper, wide, will paper 375 square yards? Ans. 500 yards.

28. If a staff 5 feet long cast a shade 6 feet, what is the height of that steeple, whose time measures 150 feet?

shade at the same

Ans. 115 feet.