X. Practical Approximations.

Without the aid of a pencil (except for writing results) give approximate answers, sufficiently accurate for many practical purposes, to the following problems:

1. What is the area of a circle 20 inches in diameter ? 2. What is the volume of a 12-inch globe?

3. What is the circumference of a circle that is 40 rods in diameter ?

4. What is the capacity, in gallons, of a tank 6 ft. by 5 ft. by 2 ft.?

5. Is the capacity of a cylindrical pail 6 inches in diameter and 5 inches deep, more or less than a gallon?

6. A piece of land 41 rods by 24 rods is how many acres? 7. What is the capacity in barrels (311⁄2 gal.) of a tank 4 ft. by 4 ft. by 2 ft.?

8. What is the weight of one cord of green hickory wood? 9. What is the weight of a stick of seasoned white pine timber 12 in. by 12 in. and 30 feet long?

10. What is the weight of the water that will fill a cylindrical tank that is 8 feet in diameter and 8 feet deep?

11. A circular mile race track encloses how many acres? 12. If the six-foot drive wheel of a locomotive makes 840 revolutions in moving a certain distance, how many revolutions will a seven-foot wheel make in moving the same distance?

13. Twenty-four kilometers is how many miles?

14. Forty-two kilograms is how many pounds?

15. A 2-inch rainfall makes how many barrels of water to the acre?

16. A certain roof is 40 feet long and, measured horizontally, 24 feet in width. A 2-inch rainfall should give how many inches in depth in a cistern that receives the water from this roof, the cistern being 6 feet long and 4 feet wide?

XI. Puzzling Problems.

1. If a person traveling as expeditiously as possible from Boston to San Francisco, should mail a letter to his friend in Boston every day at noon, how often would the letters be received in Boston?

2. If a man and a boy, the boy doing exactly one-half as much work as the man, can hoe one and one-half acres of corn in one and one-half days, how many acres can 6 men hoe in 6 days?

3. John and James sold apples together. The first day they sold 60 apples at the rate of 5 apples for 2 cents, and received 24 cents. The second day they divided the apples. John took 30 of the larger apples and sold them at the rate of 2 for 1 cent. James took the remaining 30 apples and sold them at the rate of 3 for one cent. They received 25 cents. Why did they receive one cent more the second day than the first?

The

4. A pile of four-foot wood stands upon a hill-side. pile is 8 feet long (measured on the ground), and 4 feet high (measured vertically). Does the pile contain one cord?

5. A man had shingles enough to cover his house if he laid them 4 inches to the weather. He laid them 4 inches to the weather. What part of the shingles provided remained? Explain.

6. If on a line of railroad connecting Chicago and San Francisco one passenger train leaves Chicago daily at 6 o'clock A.M., and makes the journey to San Francisco in exactly five days, and one train leaves San Francisco daily at 6 o'clock P.M., and makes the journey to Chicago in exactly five days, (a) a person taking the train at Chicago will meet how many passenger trains while going to San Francisco? (b) How many trains of passenger cars required to equip the road?

BUSINESS PROBLEMS.

The Extension Clerk.

NOTE.-In large wholesale houses, clerks are sometimes employed in extending bills. These clerks receive the bills upon which the amount, description, and price of the goods sold, are given, and extend each line; that is, they carry into the proper place the value of each purchase. They also add the columns of figures representing these values.

1. Copy and extend the above bill.

The dashes indicate where the extension figures should appear. Put the amount of the bill, in column B opposite the last line in column A.

*261 lb. @ 7¢ a pound. case; $1.10 a dozen. § 764 lb.

+325 lb. @ 70 per cwt.

$2.00 a bushel.

5 cases; 2 doz. in a 1726 lb. @ $5.51 per cwt.

1. Copy, extend, and find the amount of the above bill. 2. How much must Mr. Dodge remit if paid in 10 days? 3. In 30 days? 4. In 60 days? 5. In 75 days?

NOTE. — In this bill the list price of all books upon which the discount is exactly 25%, should appear in column A. The net price of all other books is carried directly into column B. The sum of column A less 25% of itself is carried into column B. The sum of column B is the amount of the bill; but a special discount, as shown at the top of the bill, is allowed for prompt payment. The dashes indicate where the extension figures should appear.

*Two books @ $4.50 each.

+ $1.25 less 15% of itself.

25% of the footing of column A. || The footing of column A less 25% of itself.

1. Copy, extend, and find the amount of the above bill.

NOTE. In this bill list prices are given. In column A, values according to list prices are to appear; in column B, net values. The dashes indicate where the extension figures should appear.

*24 1⁄2-inch cast iron ells at 6¢ each.

+507 feet, 0 inches.

a & b. The footing should appear at a; the footing, less the discount, at b.