MENTAL EXERCISES.

MISCELLANEOUS EXAMPLES.

1. How much will 9 eggs cost, at 20 cents a dozen?

2. How much will 8 pearl buttons cost, at 75 cents a dozen? 3. What will 4 table-spoons cost, at the rate of $11.52 a gross ? 4. What will shoe-tacks cost a dozen, at the rate of $2.88 a great gross?

5. What will 8 sheets of paper cost, at 18 cents a quire?

6. What will 12 quires of paper cost, at $4 a ream?

7. What cost a gross of lead-pencils, at 50 cents a dozen? 8. What will 2 reams of sand-paper cost, at 22 cents a quire?

9. If a ream of emery-paper costs $12, what does it cost a quire? 10. What will 4 gross of pens cost, if the wholesale rate is 2 pens for a tent?

11. A vessel was sunk in 8 fathoms of water; how many feet deep

was it?

12. How many feet high is a horse which measures 15 hands high?

13. How much will 3 pecks of potatoes cost, at 80 cents a bushel? 14. When apples sell at 20 cents a peck, how much are they worth a bushel?

15. What will 3 quarts of molasses cost, at 96 cents a gallon?

16. How many vials, holding a gill each, can be filled with half a gallon of alcohol?

17. How many half-pint bottles will 2 gallons of Arnold's writing fluid fill?

18. If I pay $1.60 for a bushel of blackberries, how much is that a quart?

19. If it takes 6 buttons for 1 shirt, how many shirts will 2 gross of buttons trim?

20. The distance across a city park is 132 paces; how many rods is it?

21. What will 15 pounds of flour cost, at the rate of $4 a hundred weight?

22. A boy bought a bushel of chestnuts for $2.40, and sold them at 12 cents a quart; what did he gain?

23. I bought 30 lb. of flour for $1.50; how much is that a hun dred-weight?

24. Albert's horse is 5 feet in height; how many nands high is his horse?

25. A vessel sails 4 leagues an hour; how many hours will it take to sail 120 miles ?

WRITTEN EXERCISES.

MISCELLANEOUS EXAMPLES.

1. What will 5 tons of coal cost, at 371 a hundred ?

Ans. $37.50.

2. How many guineas in 47 pounds and 5 shillings?

Ans. 45 guineas.

3 How many pounds Avoirdupois in 105000 grains?

Ans. 15 lb.

4. At 6 a pound, what will 5 cwt. 75 lb. of sugar cost? Ans. $34.50.

5. How much will 6 barrels of flour cost, at the rate of 31 cents a pound? Ans. $416. 6. How many suits of clothes, containing 63 yd. each, can be cut out of 93 yd. of cloth? Ans. 13; 51 yd. over. 7. How many doses of medicine, each weighing 7 grains, can be made out 1 3 23 29 11 gr.? Ans. 93 doses.

8. How many cannon-balls, each weighing 41 lb. 10 oz., can be made out of a ton of iron?

Ans. 48 balls.

9. How many times will a wheel, 15 ft. 4 in. in circumference, revolve in going 50 miles?

Ans. 17217

10. Which is greater, and how much, six dozen dozen or a half a dozen dozen? Ans. 1st, by 792.

11. How many kegs, each containing 5 gal. 2 qt. 1 pt., can be filled from a tun (4 hhd.) of wine? Ans. 44.

12. How many lots of 5 A. 82 P. are there in a field containing 66 A. 24 P.? Ans. 12 lots. 13. At 13 cents a pound, how much rice can be bought for $81,250?

Ans. 312 tons. lose in 50 years by Ans. 2 yr. 30 da.

14. How much time will a person taking an hour's nap each afternoon? 15. If a comet pass through an arc of 7° 5′ a day, how long will it be in describing an arc of 270° ? Ans. 38 da. 16. How many minutes longer was January, 1860, than February of the same year? Ans. 2880 min. 17. If a physician uses on an average 53 73 19 4 gr. of drugs daily, how many did he use during February, 1876? Ans. 14 lb. 33 63 19 16 gr.

18. How long will it take to count a million at the rate of 80 per minute, working 12 hours a day? Ans. 171 da. 19. How many half-pint bottles will it take to put up 6 gallons of Arnold's writing fluid? Ans. 96. 20. How many more seconds were there in 1876 than in a solar year? (See Art. 297.) Ans. 65470.3 sec

21. How many boards, 12 ft. long, will inclose a lot 50 r3. long and 27 rd. wide, the fence being 3 boards high?

Ans. 6351. 22. How many ounces of calomel will it take to make 980 pills of 5 grains each? Ans. 103 13 29. 23. If a weekly newspaper (one sheet) has 5600 subscribers, how many reams of paper will it require in a year, not allowing for waste? Ans. 606 reams, 13 quires, 8 sheets. 24. How many minutes more in the spring of every com mon year than in the autumn ? Ans. 1440 min.

25. How many pages are there in an octavo book, the printing of which requires 20 fully printed sheets? Ans. 320. 26. Mr. A's income averages 4 cents a minute; what will it be during the three summer months? Ans. $5299.20.

27. If 32,400 steel pens are made by a factory in a day, how many gross will be made in the month of March? Ans. 6975 gross.

28. If a grocer's weights are of an oz. in a pound below the legal standard, how much does he gain fraudulently from the sale of 2 bags of Rio coffee, 116 lb. each, true weight, at 18 a pound? Ans. $0.69

29. I bought 5 T. 14 cwt. of hay in a stack, but before it was all delivered, 1 T. 3 cwt. 56 lb. were spoiled by the weather. The price originally agreed upon was $88.35; what should I pay for what I received? Ans. $70.091.

30. A New Jersey truck-raiser sold 15 bu. 3 pk. 1 qt. of strawberries, at 11 a quart, and agreed to take flour in payment at 31 a pound, as far as it would make an exact number of barrels, and the rest to be paid in cash; how many barrels and how much cash did he receive?

Ans. 8 barrels and 67.

ADDITION OF COMPOUND NUMBERS.

306. Addition of Compound Numbers is the process of finding the sum of two or more similar compound num

oers.

1. Find the sum of £7 6s. 8d.; £5 9 s. 3 d.; £14 13 & 10 d.; and £11 19s. 11 d.

OPERATON,

£ 8. d.

7

6

8

5

9

3

14

13

10

11

19 11

8

SOLUTION.-We write the numbers so that similar units shall stand in the same column, and begin at the right to add. 11 d. plus 10 d., plus 3 d., plus 8 d., are 32 d., which by réduction we find equals 2 s. and 8d.; we write the 8 d. in the pence column, and reserve the 2s. to add to the column of shillings: 2s. plus 198., plus 13 s., plus 9s., plus 6 s., are 49 s., which by reduction we find equals £2 and 9 s.; we write the 9 s. in the column of shillings, and reserve the £2 to add to the column of pounds; £2 plus £11, plus £14, plus £5, plus £7, equal £39, which we write under the pounds. Hence the following

39 9

Rule.-I. Write the compound numbers so that similar units stand in the same column.

II. Begin with the lowest denomination and add each column separately, placing the sum, when less than a unit of the next higher denomination, under the column added.

III. When the sum equals one or more units of the next higher denomination, reduce it to this denomination, write the remainder under the column added, and add the quotient obtained by reduction to the next column.

IV. Proceed in the same manner with all the columns to the last, under which write the entire sum.

Proof. The same as in addition of simple numbers. NOTE.-In writing, if any places are wanting supply them with a cipher. WRITTEN EXERCISES.

12. Find the sum of 132 sq. yd. 8 sq. ft. 120 sq. in., 246* sq. yd. 7 sq. ft. 137 sq. in., 546 sq. yd. 3 sq. ft. 129 sq. in., 765 sq. yd. 6 sq. ft. 105 sq. in., 382 sq. yd. 5 sq. ft. 126 sq. in. Ans. 2074 sq. yd. 6 sq. ft. 41 sq. in.

13. Find the sum of 16 A. 104 P. 18 sq. yd. 7 sq. ft., 25A. 116 P. 28 sq. yd. 8 sq. ft., 18 A. 139 P. 17 sq. yd. 6 sq. ft., 27 A. 106 P. 30 sq. yd. 8 sq. ft., 24 A. 155 P. 26 sq. yd. 5 sq. ft. Ans. 113 A. 144 P. 1 sq. yd. 7 sq. ft.

SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed.

14. A vintner sold to A 5 hhd. 59 gal. 3qt. 1 pt. of wine, to B 20 hhd. 45 gal. 2qt., to C 39 hhd. 58 gal. 1 pt., and had as much as be sold A remaining; how much had he at first?

Ans. 72 hhd. 34 gal. 1 qt.

15. What is the sum of 126 yr. 10 mo. 5 wk. 17 hr., 236 yr, 9 mo. 2 wk. 7 da. 18 hr. 41 min., 425 yr. 8 mo. 4 wk. 3 da. 20 hr. 16 min.. 198 yr. 7 mo. 6 wk. 19 hr. 52 min., 385 yr. 5 wk. 40 min.?

Ans. 1373 yr. 3 mo. 3 wk. 6 da. 4 h. 29 min. 16. Find the sum of 144 cu. yd. 18 cu. ft. 1329 cu. in., 275 cu. yd.

25 cu. ft. 1076 cu. in., 382 cu. yd. 17 cu. ft. 20 cu. ft. 1507 cu. in., 367 cu. yd. 21 cu. ft.

Ans. 1591 cu. yd.

1521 cu. in., 420 cu. yd. 1473 cu.

in.

23 cu. ft. 1722 cu. in.