globe, allowing it to be 25000 miles in circumference, if she sails at the rate of 2640 miles in 12 days?

Ans. 113 days. 12. If it will take 25 barrels of flour to pay a debt when flour is $5.25 a barrel, how many barrels will it take to pay the same debt when flour is worth $6.50 a barrel?

Ans. 20 barrels. 13. Borrowed of a friend 225 dollars for 30 days; I afterwards loaned him 450 dollars. What number of days must he keep the 450 dollars to balance the previous favor? Ans. 15 days.

14. A ship's company of 12 persons is supposed to have bread sufficient to last their voyage, allowing each person 12 ounces a day. They pick up a crew of 6 persons in distress, whom they permit to share their daily allowance with them. What will be the daily allowance of each person ?

Ans. 8 ounces. 15. If 2 cwt. 1 qr. 14 lbs. of sugar be worth $21.75, what will be the value of 42 cwt. 3 qrs. at the same rate?

cwt.

lbs.

cwt.

2. 1. 14: 42. 3-21.75: 391.50. Ans.

In this question, the first and second terms being compound numbers, each of them must be reduced to pounds.

16. If a piece of linen containing 21 yards is worth £3. 5s. 3d. 1qr., what will be the value of 4 pieces of linen, containing 84 yards? Ans. £13. 1s. 1d. 17. If 7 yards of ribbon are worth 6s. 8d., what is the value of 42 yards?

Ans. £2. 18. If 7 ounces of gold are worth £30, what is the value of 7 lbs. 11 ounces? Ans. £407. 2s. 10d. 14 qr. 19. Purchased 54 yds. of broadcloth, for which I paid £60. 15s.; how many yards of the same kind of cloth can I purchase with £10. 2s. 6d. ? Ans. 9 yards.

20. Purchased 25 a. 2 r. 20 rods of land, for which I paid $639.0625; what is the value of a farm containing 205 acres, supposing the land to be of the same quality?

Ans. $5112.50.

21. If of an acre of land is worth 15 dollars, what is the value of 7 of an acre?

If of an acre of land is worth 15 dollars, or a whole acre must be worth of 15 dollars, and of an acre must be

worth as much as a whole acre; hence we have the following 3rd statement.

4 of 4 of 15 = 17.50. Ans.

Pupils should be required to analyze, state, and perform each of the following problems in a similar manner.

22. If of a yard of cloth is worth $1.15, what is of a yard worth? Ans. 715 cents.

23. If of a lot of land is worth 150 dollars, what is the value of of the same lot?

24. If of a yard of cloth is worth is the value of 12 yards?

Ans. 320 dollars.
of a dollar, what
Ans. $11.655.

of grass in 11 days,

25. If 5 men can mow 724 acres how many acres can they mow in 8 days?

Ans. 5210 acres.

26. If 7 pounds of butter are worth 15 dollars, what is the value of 27 pounds? Ans. $5.30.

27. If a man perform a journey in 7 days, travelling 12 hours each day, in how many days will he perform it, if he travel but 94 hours each day?

28. If 15 yards of cloth cost $45.75, how many yards can be purchased with 366 dollars?

cts.

1ST STATEMENT.
$ cts.

45.75: 366.00 =

yds. yds.

2ND STATEMENT.
yds.

yds.

= 15: 120. Ans. 366.9 × 15=120. Ans.

29. If 12.75 acres of land are worth $255, what is the value of 102 acres of the same quality?

30. If .75 of a bushel of wheat is worth .90 of a dollar, what is the value of 24.5 bushels?

31. If 25 dollars will pay for the transportation of 5 tons 102.5 miles, what distance can 5 tons be carried for $125.375?

32. Paid $37.50 for 5 barrels of flour; how many barrels can be purchased with 450 dollars?

33. How many bushels of corn, at $.625 a bushel, will amount to as much money as 75 bushels of wheat, at $1.25 a bushel?

34. How many yards of cambric, .625 of a yard in width, will be required to line a lady's dress containing 10.75 yards, that is .875 of a yard in width?

35. If it take 4.75 yards of broadcloth that is 1.5 yards wide to make a gentleman's cloak, how many yards of silk that is only .875 of a yard wide will be required to line it?

COMPOUND RATIO AND COM

POUND

PROPORTION.

Art. 132. A COMPOUND RATIO is the ratio of the products obtained by multiplying the corresponding terms of two or more simple ratios.

ILLUSTRATION. The simple ratio of 3: 5 = 3.

The simple ratio of 4: 7.

Multiplying the terms of the ratio 3: 5 by the corresponding terms of the ratio 4: 7, we obtain the composite or compound ratio 12: 35.

Multiplying by, we obtain the same compound ratio, 1, in a fractional form.

Art. 133. Compound Proportion is the equality of two ratios, one of which is compound, and the other simple.

Every question in compound proportion always contains an odd number of terms, as five, seven, nine, &c. These terms are distinguished into terms of supposition, and terms of demand; the number of the former is always one more than that of the latter. One of the terms of supposition always has the same name, or is of a like kind, as the required term, or answer; which must always be made the third term in stating. Each of the remaining terms of supposition has its corresponding term of demand of a like kind, one of which must be made the first term of a simple ratio in stating, and the other the second.

ILLUSTRATION. 1. Suppose that 12 men can earn 600 dollars in 25 days; how many men will be required to earn 400 dollars in 20 days?

This question contains five numbers or terms; the first three are the terms of supposition, and the last two are the terms of demand.

1ST STATEMENT.

600 dollars: 400 dollars. 20 days : 25 days.

= 12 men.

12000 dollars: 10000 dollars 12 men: 10 men, the number required.

As the required term or answer is to be a number of men, we write 12, the supposed number of men, for the third term. 12 men are supposed to earn 600 dollars in 25 days, and it will require only 88 of 12 men to earn 400 dollars in the same number of days; therefore, we write 400 dollars for the second term, and 600 dollars for the first term. As the 400 dollars is to be earned in g of the number of

days, it will require 25 as many men to earn 400 dollars in of the time; therefore, we write 25 days for the second term, and 20 days for the first term.

Multiplying the terms of the first simple ratio by the corresponding terms of the second, we obtain the compound ratio 12000 dollars: 10000 dollars 12 men to the number of men required to earn 400 dollars in 20 days.

Multiplying the third term 12 by the second term 10000, the product is 120000; dividing this product by the first term 12000, the quotient is 10, the number of men required to earn 400 dollars in 20 days.

da.

2ND STATEMENT.

$

25 × 488 × 12=10, the number required to earn 400 dollars in 20 days. Reducing each fraction to its lowest terms, we have × × 12 = 10 men, the number required. From the above illustrations we derive the following

RULE. Write that term of supposition which has the same name, or is of the same kind, as the required term or answer, for the third term.

Then take one of the other terms of supposition and its corresponding term of demand of the same kind, and consider whether an answer depending on these terms alone must be greater or less than the third term, and write one of them for a second term, or numerator of a fraction, and the other for a first term, or denominator, as directed in simple proportion. Arrange all the remaining corresponding terms of supposition and demand in a similar manner.

Then find the product of all the second terms or numerators; find also the product of all the first terms or denominators; multiply the third term by the product of the second terms or numerators; divide this product by the product of the first terms or denominators, the quotient will be the answer or term required.

The terms of each simple ratio, if of different denominations, must be reduced to the same, and the third term must be reduced to the lowest denomination in it.

Art. 134. It will be perceived that all the second terms, or numerators, and the third term also, are factors of a dividend, and that all the first terms, or denominators, are factors of a divisor.

Since diminishing the dividend and divisor equally does not alter the quotient, therefore all equal factors of the divi

dend and divisor may be crossed or cancelled, and not used in the operation.

When any two factors, one of them being a factor of the dividend, and the other a factor of the divisor, have a common measure, both may be crossed, and then divided by that common measure, and the quotients retained.

2. If 6 men can build a wall 20 feet long, 6 feet high, and 4 feet thick, in 16 days, in what number of days will 24 men build a wall 200 feet long, 8 feet high, and 6 feet thick?

Cancelling all equal factors, we have only to multiply the third term, 16 days, by 5, the product is the number of days required.

2ND STATEMENT.

da.

da.

X & X 200 X X 16 = 80. Ans.

Reducing each of the above fractions to its lowest terms, we have

3 4
X

da.

da.

X-X 16=80. Ans.

1 4

Cancelling all equal factors, we have

1 1 5 1 da.

da.

X XXX 16=80. Ans.

In the above question, 6 men are supposed to build a wall 20 feet long, 6 feet high, and 4 feet thick, in 16 days; these five numbers or terms are the terms of supposition. It is required to find the number of days in which 24 men can build a wall 200 feet long, 8 feet high, and 6 feet thick; these four numbers or terms are the terms of demand.

As the answer is required to be a number of days, we write 16 days, the term of supposition of a like kind, for the third term.

Comparing 6 men, a term of supposition, with 24 men, its corresponding term of demand, we find that 24 men is 24 of 6 men, hence it will take 24 men only of 16 days to perform the same work; therefore we write 6 for the second term and 24 for the first, in the first statement, and 6 for the numerator of a fraction and 24 for the denominator, in the second statement.

Comparing 20 feet in length, a term of supposition, with 200 feet in length, its corresponding term of demand, we find that 200 feet is 200 of 20 feet; hence it will take 200 as