20. James and John gathered 60 melons: James gathered 3 times as many as John; how many did each gather?

SOLUTION. Since James gathered 3 times as many as John, 3 times John's number equals James' number, which, added to John's, is 4 times John's, or both. If 4 times John's number is 60, his number is of 60, or 15, and James' number is 3 times 15, or 45.

21. Two boys have 30 marbles: the first has twice as many as the second; how many has each ?

22. Mary and Ella gathered 60 roses: Ella gathered 2 times as many as Mary; how many did each gather?

23. The ages of two men are 45 years: one is as old as the other; how old is each ?

24. If Charles and Simon gather 24 quarts of berries, and Charles gathers 13 times as many as Simon, how many quarts does each gather?

25. Two men have $3400: of what the first has equals 3 of what the second has; how much money has each?

26. A house, a farm, and a store cost $12,000: the farm cost twice as much as the house, and the store 3 times as much as the house; how much did each cost?

27. A man bought three properties: the second cost twice as much as the first, and the third 3 times as much as the second; what was the cost of each, if they together cost $13,500?

28. Three times Henry's money equals 4 times Arthur's: they together have $140; how much has each?

29. Two boys sold 90 tickets; how many did each sell if 4 times what the first sold equals 5 times what the second sold?

30. The sum of two fractions is 1 of the first equals of the second; what are the fractions?

31. Bought a hen, a duck, and a turkey: the duck cost 15 cents less than the hen, and the turkey 3 times as much as the duck; what was the price of each, if they together cost

PARTNERSHIP.

1. Two men in partnership gain $600. B owns of the stock, lacking $100, and his gain is $400; how much stock has each ?

SOLUTION.-If A had owned & of the stock, his gain would have been of $600, or $450; but he gained only $400, therefore the $100 would have gained the difference between $450 and $400, or $50. If it requires $100 to gain $50, it requires $2 to gain $1, and to gain $600 it requires 600 times $2, or $1200; hence A had & of $1200, or $900, less $100, which equals $800; and B, $1200 minus $800, or $400.

2. Mr. Smith and Mr. Handy enter into partnership and gain $300. Mr. Smith owns of the stock, less $200, and his share of the gain is $60; how much stock does each own?

3. Mr. A and Mr. B gain in partnership $320. Mr. A owns of the stock, + $60, and his share of the gain is $110; what amount of stock has each?

4. C and D bought a store, and in selling it cleared $1500. C owned of it, less $600, and his share of the gain was $600; what amount did each pay?

5. Charles and Henry agree to plow some land for $60. Charles plowed of the land and 10 acres more, and received $40; how much did each plow?

6. If a man builds of a wall and 6 rods more and receives $48, how long is the wall, if the total cost of building it is $120?

THE METRIC SYSTEM.

The Metric System is a decimal system of weights and measures having the meter for its base or unit.

The system was first adopted in France in 1795, and it is now used in France, Germany, Spain, Portugal, Belgium, Greece, Mexico, Brazil, and most of the other states of South. America.

Its use is authorized by law also in Great Britain and the United States. The system is used chiefly by scientific men, as being the simplest system of weights and measures in existence. The principal metric units are

1. The Meter, for lengths.

2. The Are, or square meter, for surfaces.

3. The Stere, or cubic meter, for volumes.

4. The Liter (lee'ter), or cubic decimeter, for capacities. 5. The Gram, for weights.

The Meter, the primary unit of the system, is 39 inches. The names of the denominations lower than a unit are indicated by prefixing the Latin words milli (1000), centi (100), and deci () to the unit; thus, millimeters, centimeters, etc.

The names of the denominations greater or higher than a unit are formed by prefixing the Greek terms deca (10), hecto (100), kilo (1000), and myria (10,000) to the unit; thus, decagrams, hectograms, etc.

Metric numbers are written as decimals, with the decimal point after the unit. Thus, 15 meters and 5 centimeters is written 15.05 m. This may be read 15 and ʊ meters, or 15 meters and 5 centimeters.

The following are the tables of the metric system:

.

The Meter, a little less than 1 yd. 3g inches, is used in measuring short distances.

The Kilometer, a little less than of a mile, is used in measuring long distances.

Land is measured by the Are, about 103 sq. feet, and the Hectare, about 2 acres.

The cubic meter, or stere, used for measuring wood, embankments, etc., is about 1 cu. yard, or .2759 of a cord. The following table also is used:

4.

LIQUID OR DRY MEASURE.

The Liter is the unit of the measure of capacity. It is equal to a cube each of whose sides is equivalent to about 11 liquid quarts or

measure.

10 milliliters (ml.)

10 centiliters

10 deciliters

10 liters

10 decaliters

10 hectoliters

of a meter, and is

of a quart dry

1 decaliter

(Dl.)

1 hectoliter (Hl.)

1 kiloliter (Kl.)

The Hectoliter is used in measuring liquids, grains, fruits, and roots in large quantities. It is equal to about 25 bu. A Kiloliter is a cubic meter or stere.

5. WEIGHT.

The Gram, the unit of weight, is equal to a cube of distilled water the edge of which is Too of a meter, equal to 15.432 Troy grains in weight.

10 milligrams (mg.) = 1 centigram (cg.)