CHAPTER VIII.

MISCELLANEOUS PROBLEMS.

NOTE. The following problems do not constitute a necessary part of an elementary course in arithmetic. They are added here because of their value for review work, or for use by pupils who may be somewhat in advance of the class.

CANCELLATION.

1. How many bushels in 8 boxes of beans, each containing 20 quarts?

2. The factors of a dividend are 16, 50, and .9; of the divisor, .15, 8, and 2. What is the quotient? Divide 56 x 14.4 by 14.

3. A farmer gave 55 sheep for 11 young horses worth $60 each. What money value did he get for each sheep? of of = ?

4. How many barrels of 36 gallons each will contain as much as 12 hogsheads of 63 gallons each?

5. If 1 man can mow 6 acres of grass in a day, how many men will it take to mow 3 fields of 56 acres each?

6. At 60 cents a cord, how many days will it take a man to earn $75.00, if he saws 2 cords of wood a day?

7. If a turkey weighing 10 pounds cost $1.68, what will be the cost of one that weighs 15 pounds?

COMMON FRACTIONS.

1. At of a dollar per yard, how many yards of cloth can be bought for of a dollar?

2. At the rate of 2 dollars for 3 baskets of peaches, what is that per basket?

3. If I use of a pound of sugar in making one cake, how many cakes can I make with 2 pounds?

4. Helen divided 1 pounds of nuts equally among 5 playmates. What part of a pound did each receive?

5. Horace divided 5 apples equally among 6 boys. What part of one apple did each receive? 6. At 1 dollars each, how many lamps can be bought for 6 dollars?

7. A man divided 8 dollars among his children, giving them 1 dollars apiece. How many children had he?

8. At 2 dollars a box, how many boxes of lemons can be bought for 6 dollars?

9. At of a dollar per yard, how many yards of ribbon can be bought for 2 dollars?

10. A gentleman gave away of the books in his library, lent of the remainder, and sold of what was left. He then had 360 books remaining. How many had he at first?

11. If a lady spends 4 dollars per month for car fare, in what time will she spend $271?

DECIMAL FRACTIONS.

1. The owner of a schooner sells .35 of the ves sel to the captain. What part does he still own? 2. The minuend is 67.081. What must the subtrahend be to leave a remainder of 56.009 ?

3. The less of two numbers is 3207.56 and their difference is 978.756. Find the greater number. 4. A. owns iron foundry and sells .75 of his share for $2100. What is the value of the whole foundry?

of an

5. What is the gain on 5000 bushels of wheat bought in Chicago at $1.4375 per bushel and sold in New York at $1.625 per bushel, allowing 15 cents per bushel for transportation?

6. A flour merchant bought 137 barrels of flour at $7.875 per barrel. He sold 89 barrels at $9.378 per barrel, and the remainder brought only $5.80 per barrel. What was his gain?

7. Two men start from the same place and travel in opposite directions. One travels 119.33 miles a day, and the other 123.75 miles a day. How far will they be apart at the end of six days?

8. I sold .36 of my land for $900. How much is the remainder of it worth at the same rate?

9. Divide $3679.94 by $5.004.

10. Divide 6504.5 yards by 5.06 yards.

MENSURATION.

1. Supposing each child in a schoolroom ought to have 80 cubic feet of air, how many children should sit in a room which is 20 feet long, 18 feet wide, and 12 feet high?

2. How many tiles, each 3 inches square, will cover the space around a fireplace 5 feet long and 3 feet wide?

3. The walk from our kitchen door to the stable is 75 feet long and 4.5 feet wide. How many bricks in it, each brick being 8 inches by 4 inches? 4. How many times is 4 cubic inches contained in a four-inch cube?

5. How many cubic inch blocks will a box contain which is 1 ft. long, ft. deep, and 8 in. wide?

40 ft.

6. How many gallons will fill a tank 8 feet by 6 feet by 5 feet? (231 cubic inches in a gallon.) 7. How many loads of earth must be removed in digging a cellar of the dimensions given in

the diagram.

(A cubic yard is understood to be a load.)

8 ft. deep.

Papering and Plastering.

101 ft.

20 ft.

30 ft.

1. How many square yards of plastering in the 4 walls of a room 14 ft. long, 121 ft. wide, and 8 ft. high, if no allowance is made for doors and windows?

2. How many square yards of plastering in the ceiling of a room 15 feet long by 14 feet wide ? If this room is 9 feet high above the baseboard, how many square yards in the walls and ceiling together, no allowance for doors and windows?

3. How many square yards of plastering in the walls and ceiling of a room 16 feet long, 14 feet wide, and 9 feet high, if 14 square yards be allowed for doors, windows, and baseboard?

4. How many rolls of paper 18 in. wide will be required to paper the walls of a room 20 ft. long, 19 ft. wide, and 9 ft. high, deducting 60 sq. ft. for the surface of one door and two windows, and allowing a roll for waste in matching?

(The height is measured from the top of the baseboard.)

NOTE 1. The cheapest wall paper is 18 in. wide. In American paper, the single rolls are 8 yd. long; the double rolls are 16 yd. long. A single roll is understood unless a double roll is given in the problem. There are 36 sq. ft. of covering surface in a single roll of 18 in. paper (24 ft. × 13 ft. = 36 sq. ft.).

NOTE 2. The walls of a room 20 ft. by 19 ft. and 9 ft. high, make a rectangle 78 ft. long by 9 ft. wide, which contains 702 sq. ft. Deducting 60 sq. ft. for doors and windows (20 sq. ft. for each), there are 642 sq. ft. 642 sq. ft. 36 sq. ft. 17. Adding a roll for waste, 18 rolls is the amount required.

5. How many rolls of paper 30 in. wide will be required to paper the walls and ceiling of a room 30 ft. long, 26 ft. wide, and 10 ft. high, allow ing 120 sq. ft. for doors and windows, and of a roll for waste?

(How many square feet of surface in a single roll of 30 in. paper?)