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MISCELLANEOUS PROBLEMS.

577. Oral Problems. 1. A merchant, in selling a book, gained 2 pence, which was .2 of the cost.

did the book cost the merchant ?

How many pence

2. If John's money, $5.25, is .05 as much as Edward's money, how much money has Edward ?

3. Thomas is 8 years 4 months old, and his father is 50 years old. Thomas' age is what decimal part of his father's

age ?

4. If a box contains 200 lb. of coal, how many boxes of the same size will be required to hold 2 T. 4 cwt.?

5. Bought 5 lb. 4 oz. of lard at 16 ¢ per lb.; paid for it with a dollar bill. What change is due ?

6. If 3 pecks of nuts cost $.96, what do the nuts cost per bushel?

7. How many 3 ft. cubes can be cut from a block 9 feet long, 6 feet high and 3 feet wide?

8. Bought beans for 12 ¢ a half peck. How much will be lost per bushel, if 4 bushels are sold for $3.60 ?

9. If a metal is worth 8 per pound, what will 4 T. cost? 10. A man has 2 A. of land and sells 120 square rods. How many acres has he left ?.

11. A room is 8 yd. long and 15 ft. high. What decimal part of the length is the height?

12. What will it cost to carpet a passage-way .75 of a yard wide by 12 feet long with 27 inch-wide carpet, at $3 per yard?

13. Bought cloth at $5 per yard, and sold it so as to gain .05 of the cost. How many yards must be sold to gain $10? 14. If .625 of a pound of tea costs $.37, what will a pound cost?

15. A piece of timber contains 108 cu. ft. Its width is 4 feet and its thickness, 36 inches. What is the length in feet

16. What is the number of board feet in a plank 8 feet long, 6 inches wide and 3 inches thick?

17. What is the width of each board, if 2 similar boards contain 96 board feet, the length of each being 6 feet and the thickness 2 inches ?

18. What is the cost of a yard of cloth, if .75 of a yard cost $2.70 ?

19. If a boy earns $.663 per day, how much will he earn in 4 weeks of 6 working days each ?

20. What is the length of a rectangular field 40 rods wide, and containing 20 A.?

21. How many yards of matting 1 yard wide will cover a floor 12 feet long by 9 feet wide?

22. What is the price of a plank 10 feet long, 6 feet wide, 11⁄2 inches thick, if a thousand board feet cost $30 ?

23. At 6 per yard, how much will it cost to border with lace a table cover 5 feet long and 4 feet wide?

24. What will 1,200 feet of boards cost at $25 per M ?

578. Written Problems.—1. If the driving wheel of a locomotive is 11 ft. 8 in. in circumference and makes 12,000 turns in travelling from one city to another, what is the distance in miles between the cities?

2. A man having a farm of 200 acres, gives to his son and .45 of the remainder to his daughter. He gives to a village a church lot 10 rods wide by 12 rods long. The rest he gave to his wife. How much does his wife receive?

3. A room contains 4,200 cu. ft. The width is 5 yards and the height 14 feet. What is the length ?

4. How many steps, 2 feet 6 inches each, will be taken in walking around a farm 1 mile square?

5. How many board feet are there in a piece of timber 18 feet long, 21⁄2 inches thick, 14 inches wide at one end, and 18 inches at the other?

6. The distance from New York to New Haven being 73 mi. 80 rd., at what rate does a train travel, to cover the distance in 2 hours 10 minutes ?

7. A grocer has 209 bu. of pears. How much at 15 ¢ each must he pay for a sufficient number of barrels to contain the pears, each barrel holding 2 bu. 3 pk.?

8. What is the length of a pole standing .125 of its length in mud, 18 feet in water, and of its length in the air?

9. A man's garden, which is 8 rods long and 99 feet wide, is .08 of his land. How many acres of land has he?

10. If a man buys 16 gallons of wine for $104, and retails it at $.85 per pint, how much does he gain on 3 gallons?

11. What is the value of a piece of timber 25 feet long, 16 inches square, at $.12 per cubic foot?

12. How many bricks with mortar will it take to make a wall around a garden 6 rods long and 4 rods wide, the wall being 9 feet high and 3 feet 6 inches thick?

13. What is the cost of 15 planks, each 12 feet long, 14 inches wide, 3 inches thick at $45 per M. board feet?

579. Make receipted bills for the following statements :

1. Cincinnati, May 28, 1882. Edward Price bought of Jas. McFarland, 4 bbl. New Orleans sugar @ $6.25; 3 sacks coffee @ $31.50; 2 tubs butter, each containing 56 lb., @ $.19 per pound; 15 lb. cheese @ $.18; 80 lb. ham@ $.11 a pound.

2. A farmer sold 175 bushels of corn @ $.79 a bushel; 197 bushels wheat @ $1.19 a bushel; 50 bushels oats @ $.60 a bushel; 3 tons hay @ $14.75 a ton.

3. New York, July 5, 1885.-John Hopkins bought of William Warren & Co. 3 reams extra foolscap @ $2.15 per ream; 2,000 envelopes @ $1.60 per M.; 6 gross lead pencils @ $3.20 per gross; 10 boxes steel pens @ $.45 per box, 500 slate pencils $1.75 per hundred.

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4. Chicago, Dec. 20, 1875. Albert Longley bought of Robert Upton & Co. 56 yd. Hope Muslin @ $.091⁄2 a yard; 48 yards French Cambric @ $.28 a yard; 2 dozen Lisle Hose @ $4.00 a dozen; 24 yards Linen Lawn @ $.163 a yard ; 15 yards India Mull @ $.633 a yard.

5. Henry Farnham, carpenter, labored 42 days @ $2.25 a day for Frank Elmore, and supplied the following materials: 45 pounds of nails at $.05 a pound; 1,500 bd. ft. lumber $12.40 a thousand.

580. Copy, and complete the following:

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What is the amount on hand at the end of the month?

NOTE. The account is debited (Dr.) to the extent of items received, and credited (Cr.) by items paid out.

PERCENTAGE.

581. 1. John had $1 and spent 14. What part of his money did he spend?

2. Mary bought a yard of elastic for 2, and paid for it with a dollar. What part of her dollar did she spend ? 3. A man invested money and received a dividend of 3 ¢ on every dollar. What part of a dollar did each dollar earn? NOTE. The answers to the above should be expressed as common and as decimal fractions.

582. The unit of exchange in the United States is the dollar ($1.00), and earnings, profits, losses, interest, etc., are reckoned as so many cents on the dollar; that is, as so many cents on the hundred cents, or by the hundred.

583. Percentage is a process of reckoning by the hundred.

584. Percentage is, also, the result obtained by taking so many hundredths of a number.

18 is a percentage of 24, being .75 of 24.

585. Per cent. is an abbreviation of the Latin phrase per centum, meaning by the hundred.

586. The rate per cent. is the number of the hundredths taken.

12 is 5 per cent. of 240, as it is .05 of 240 ; 5 being the rate per cent. 587. The sign of per cent., %, is used with the rate per cent. expressed as a whole number; thus, .05 or 5 per cent. is written 5%; .163 or 163 per cent. is written 163 %.

588. The number of which a percentage is taken is called the base.

If 5 per cent. of 240 is to be found, 240 is called the base. The base is always 100 per cent.. as any number is 100% of (1.00 ×) itself.

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