withdraws $1000. The profits amount to $1500; what is each partner's share of the same?

Ans. $576.923', $403.846', $519.23'.

19. A gentleman bequeathed the sum of $5000 to his widow, son, and daughter, in the proportion of,, and . The widow dying soon after, the whole sum was divided in due proportion between the two children; how much did each receive? Ans. $27773, and $22223.

20. How many pounds of tea at 85cts. a pound, and at 90cts. a pound, must be mixed with 5lb. at $1 a pound, that the mixture may be worth 94cts. a pound?

The proportions of the three ingredients for a mixture at the mean rate 94 cents, will be found to be,

6lb. at 85c. to 6lb. at 90c. and 137b. at $1, (151); then 1376., the term found for the rate whose quantity is given,: 5lb., that given quantity, : : 67b, the term found for any other rate, the quantity required at that rate.

Ans. 2lb. of each.

21. How many ounces of gold which is 23 carats fine, and how many 20 carats fine must be compounded with 8oz. which is 18 carats fine, that the compound may be 22 carats fine?

A carat is a weight of 4 grains; but the term is also used as above in expressing the degree of purity or fineness of gold. Thus when pure gold is combined with some baser metal, called alloy; if 20 parts in every 24 of the compound be pure gold, the alloyed gold is said to be 20 carats fine; and so for other numbers.

Ans. 48oz. of the first, and 8oz. of the second.

22. How many gallons of brandy at 25cts. per gallon, and how much water must be mixed with 5 gallons of brandy at 40cts. per gallon, that the adulterated compound may rate at 30 cents per gallon? Ans. 1 gal. of each.

23. How many gallons of vinegar at 20 cents a gal., and at 50 cents a gal. should be mixed with 4 gal. at 25 cents a gal. and 2 gal. at 16 cents a gal., that the whole may be worth 28 cents a gallon?

The 4 gal. and the 2 gal. together amount to 132 cents; hence these 6 gal. average 22 cents per gallon. By substituting 6 gallons at 22 cents for the 4 gal. and 2 gal. at their respective rates, the question becomes of the same kind as the 20th.

Ans. 6gal., and 3gal.

24. A farmer wishes to mix 10bu. of corn at 35 cents per bu., and 8bu. of rye at 40 cents per bu. with such a quantity of oats at 25 cents per bushel that the whole may be worth $0.33 per bushel. What must be the quantity of oats? Ans. 83 bushels.

25. A vintner wishes to mix wines at $0.75 and $1.25 per gallon in such proportion and quantities as to produce 100 gal. worth $0.87 per gallon. What quantities of the two kinds must be taken?

The proportion of the two kinds for a mixture at the mean rate 87 cents, is,

371gal. and 12gal. (151);

then 37+12: 37: 100: the quantity of the first kind; and 37+12:12:: 100: the quantity of the 2d kind. Ans. 75gal. and 25gal. 26. How many pounds of each of three different kinds of coffee, rating at 12 cents, 13 cents, and 15 cents per pound, must be taken for a mixture of 100lb. which shall rate at 14 Ans. 25lb., 25lb. and 50lb.

cents per

lb.?

27. Allowing a mechanic to earn $62.87 in a month, by working 94 hours per day, what ought he to earn in 3 months by working 11 hours per day? Ans. $234.50'.

28. If 50bu. of wheat be exchanged for 80bu. of rye, and 3bu. of rye for 4bu. of corn, and 10bu. of corn for 12bu. 3pk. of oats, and 3bu. of oats be worth $1; what is the value of 100bu. of wheat? Ans. $92.373'.

29. Three pipes of equal size will fill a cistern with water in 13h. 40m. In how many hours would 5 such pipes fill a cistern whose capacity is 21 times that of the first one?

Ans. 20 hours.

30. A contractor engaged to pave 15 miles of road in 12 months, and for that purpose employed 100 men. Seven months have now elapsed, and but 6 miles of the road have been completed; how many more men must be employed, to finish the work in the time prescribed? Ans. 110 men.

31. If 10lb. at London be equivalent to 976. at Amsterdam, and 45lb. at Amsterdam to 497b. at Bruges, and 9816. at Bruges to 1167b. at Dantzic; how many pounds at Dantzic are equivalent to 112 pounds at London?

Ans. 129.92 pounds.

32. If 1 ells of Hamburg make 1 ell in Holland, and 7 ells in Holland make 4 in France, and 7 in France make 5 yards in England; how many yards in England are equivalent to 588 ells at Hamburg? Ans. 200 yards.

CHAPTER VIII.

PERCENTAGE, AND ITS

APPLICATIONS.

PERCENTAGE.

(158.) PERCENTAGE is an allowance at a certain rate for every hundred.

Per centum, or its contraction per cent., is Latin, and signifies by the hundred.

every

One per cent. on any number is one for hundred; two per cent. is two for every hundred; three per cent. is

(159.) The ratio of Percentage is the ratio of the rate per cent. to 100, and is therefore equal to the rate per unit.

Thus the ratio of percentage for 4 per cent. is, or .04, which is plainly the rate for each unit of the quantity on which the percentage would be computed.

What is the ratio of Percentage for 1 per cent.? For 3 per cent? For per cent. ? For 7 per cent.? For 9 per cent.? For 10 per cent.? For 12 per cent. ?

(160.) The ratio of Percentage is usually expressed decimally; and the proper decimal may always be found by dividing the rate per cent. by 100.

What is the ratio of Percentage for 14 per cent. For 1 per cent. ? For per cent.? For 2 per cent. For per cent.? For 3 per cent.?

Basis of Percentage.

(161.) The number or quantity on which Percentage is computed, at any given rate, may be called the Basis of percentage.

Thus when we say 2 per cent. on $300, the basis of percentage is $300.

If the Rate per cent. is 2, and the amount of Percentage $4, what is the basis of percentage? If the Rate per cent. is 3, and the amount of Percentage $9, what is the basis of percentage? If the rate per cent. is 4, and the amount of Percentage $20, what is the basis of percentage?

Percentage, in its simpler forms, is applied to Profit and Loss in trade, Taxes, Duties, Insurance, Commission, Stocks, &c.

(162.) TAXES

Are charges imposed by Law on property, and frequently on persons, for public purposes.

A poll or capitation tax is a tax on the person, without regard to property.

A tax on property is sometimes specific, that is, a specified sum on certain articles; but it is most commonly ad valorem, or a specified per centum on the value.

(Ad valorem is Latin, and means according to value).

(163.) DUTIES

Are charges, either specific or ad valorem, imposed by Law on imported goods, for purposes of revenue. They are paid in the Custom Houses at the ports of entry.

The invoice is a written statement of the articles and their cost.