months; and to F $500, payable in 4 years; now, what would be the equated time for paying the whole? A. 221398 months.

Questions on the foregoing.

1. A man bought a barrel of flour for 2£ 15 s. 6 d., a hhd. of molasses for 6£ 15 s., and a barrel of brandy for 8£ 15 s.; what did the whole cost? A. 18£ 5 s. 6 d.

2. What will 9600 yards of cloth cost, at $,50 a yard? (4800) At $,33? (3200) At $,25? (2400) At $,20? (1920) At $,163? (1600) At $,12? (1200) At $,64? (600) At $,5? (480). A. $16200.

3. What is the product of 2 s. 6 d. multiplied by 2? (5) By 4? (10) By 7? (17-6) By 10? (1-5) By 12? (1-10)` A. 4£ 78. 6 d.

4. Divide 21£ 19 s. 9 d. equally among 6 men? A. 3£ 13 s. 3 d.

5. Reduce,, and, to the least common denominator. A 18, 18, 2o.

9409

6. Change 2000 francs to federal money. A. $375.

7. 1850+,3+1880 +673 +100000. A. 673,37505. 8. Change 4500£, English or sterling money, to dollars of 4s 6 d. each. A. $20000.

9. What is the interest of $21,20 for 6 months? (636) For 3 months 15 days? (371) For 1 month? (159) For 10 days? (35) For 5 days? (17) For 4 days? (14) A. $1,23 2+.

10. What is the amount of $300, at 7 per cent., for 1 year? (321) At 3 per cent.? (309) At 5 per cent.? (31650) At 93 per cent.? (32925) At 12 per cent.? (33750) A. $1613,25

11. What is the discount of $315 for 10 months, at 6 per cent.? (15) Of $550 for 1 yr. 8 mo.? (50) Of $2660 for 5 yrs. 6 mo.? (660) Of $121,402 for 8 yrs. 4 mo. 15 da.? (40602) A. $765,602.

12. What is the compound interest of $560 for 4 yrs.? (146987) For 2 yrs. 6 mo.? (88092) For 3 yrs.? (106968) A. 342,047. 13. A merchant bought goods amounting to $368,925 ready money, and sold them again for $488,75, payable in 2 yrs. 6 mo.; how much did he gain, discounting at per cent.? (Find the present worth of $488,75 first, then subtract to find the gain.) A. $56,07 5. 14. Bought corn for $,60, and sold it for $,72; what was the gain per cent.? A. 20 per cent.

15. Bought 40 gallons of molasses, at 27 cents a gallon; but, by accident, 4 gallons leaked out; at what rate must I sell the remainder per gallon to lose nothing? and how much to gain on the whole cost 20 per cent. ?

A. 30 ets. ; and, to gain 20 per cent,

36 cts.

RULE OF THREE,

OR

SIMPLE PROPORTION.

↑ LXXIII. 1. What will 3 yds. of cloth come to at 20 cents a yard? What will 5 yards? Will 7? 8? 12?

2. If 2 gallons of molasses cost 50 cents, what will 3 gallons cost? (Find what 1 gallon will cost first. It is 25 cents. Then, 3 gallons are 3 times 25, =75 cents. Proceed in the same manner with other sums of like nature.) What will 5 gallons cost? What will 8?

3. If 4 lbs. of sugar cost 48 cents, what will 2 lbs. cost? (Find what 1 lb. will cost first.) What will 6 lbs. cost? What will 8? What will 12? What will 20?

4. If 2 bushels of corn cost a dollar, how much is it a bushel? What will 3 bushels cost? What will 4? What will 6? What will 8?

5. If 20 yards of cloth cost 60 cents, how much is it a yard? What will 6 cents buy? Will 18 cents buy? Will 30 cents? Will 90? Will 300?

6. How many pounds of cheese will 12 cents buy, if 4 lbs. cost 48 cents? How many will 24 cents buy? How many will 60 cents? How many will 108 cents?

7. If 4 dollars buy 2 barrels of cider, how many barrels will 6 dollars buy? (Find the value of 1 first.) How many will 8 dollars buy? How many will 12? How many will 24? How many will 36? How many will 48? How many will 60? How many will 100? How many will 150? How many will 300? How many will 400? How many will 500? How many will 800? How many will 2000 ? How many will 3000 ? many will 40000 ?

How 8. If you pay 16 cents for 4 oranges, how many cents will buy 6? How many 36? How many 48? How many 60? 9. If 100 oranges cost 400 cents, how many cents will 4 cost? What will 8 cost? What will 25 cost? What will 30 cost? What will 50 cost?

10. If 4 tons of hay will keep 2 cattle over the winter, how many tons will keep 6 cattle the same time? How many 8? How many 10? How many 20 ? How many 40 ? many 60? How many 80 ?

How

11. If 500 cattle eat 1000 tons of hay in one winter, what will 2 cattle cat? What will 3?

What will 5?

20? What will 50? What will 200 ?

What will

12. If 2 penknives cost 25 cents, what will 3 cost? What will 4 ? What will 8? What will 12 What will 16?

13. If you pay 26 cents for 2 inkstands, how many cents will 5? 6? 7? 8? 9? 10?

buy 3?

30?

40 ?

Will buy 4?

20 ?

14. If of a yard of broadcloth cost 4 dollars, what will cost? (If cost 4 dollars, will cost 2 dollars.) What will ? What? What? What? What 1? What 1? What 18? What 1? What 1? What 18? What? (If make 1 yard, then 1 yard and will of a yard cost? What? What? What? What 3 yards?

For 3?

What 2 yards? are §.) What What 1?

15. The interest of 100 dollars for 1 year is 6 dollars at 6 per cent.; what is it for 2 years? For 9 For 12? For 20?

For 5? For 7?

16. If 6 men can do a piece of work in 12 days, how long will it take 1 man to do the same? (1 man will be 6 times as long as 6.) How long will it take 2 men? (2 men will do

it quicker than 1 man.) 3 men ? 12 men?

17 If 4 men build a wall in 20 days, how many men would it require to build the same in 40 days? (as many men.) In 80 days?

After the same manner perform the following

Exercises for the Slate.

1. If 20 yards of cloth cost $40, what will 8 yards cost?

1 yard is of $40; that is, 4020 = $2 a yard; then, 8 yards are 8 X2=$16, Ans.

2. What can you buy 15 tons of hay for, if 3 tons cost $36? (Find what 1 ton will cost first.) A. $180.

3. If 2 bushels of oats cost 40 cents, what will 24 bushels cost? A. $4,80.

4. What will 25 lbs. of sugar cost, at 17 cents a pound? 17 X 25 $4,25, Ans. 5. If $4,25 buy 25 lbs. of sugar, how much is it a pound? A. 17 cents.

6. If 3 pair of shoes cost $4,50, what will 12 pair cost? (18) What will 8? (12) What will 15? (2250) What will 16? (24) A. $76,50. 7. If 2 pair of stockings cost 50 cents, what will 3 pair cost? (75) What will 15? (375) What will 25? (625) What will 80 (20) What will 96? (24) What will 267? (6675)

A. $121,50. 8. What will 600 bushels of rye cost, at 84 cents a bushel? (504) What will 10? (840) What will 40? (3360)

What

will 800? (672) What will 1000? (840) What will 2? (168)

A. $2059,68.

9. If 60 cents buy 4 lbs. of tobacco, how much will 30 cents buy? (2) How much will 90 cents? (6) How much will 120 cents? (8) How much will $2,10? (14) How much will $2,40? (16) A. 46 lbs.

10. If 1 pair of gloves cost 75 cents, what will 1 dozen pair cost? (9) What will 1 doz.? (1350) What will 2 doz. ? (18) What will 2 doz.? (2250) What will 3 doz.? (27)

11. If 3 dcz pair of shoes cost cost? (75) What will 2 doz.? (18) What will 14 doz.? (1350)

A. $90. 27 dollars, what will 1 pair (2250) What will 2 doz. ? What will 1 doz.? (9)

(35)

A. $63,75. 12. If 5 tons of hay will keep 25 sheep over the winter, how many sheep can be kept on 7 tons, at the same rate? On 8 tons? (40) On 15 tons? (75) On 60 tons ? (300) On 80? (400). A. 850.

13. Boarding at $2,25 a week, how long will $9 last me? (4) How long will $13,50? (6) How long will $18? (8) How long will $20,25? (9) How long will $49,50? (22) A. 49 weeks.

14. If a man receive $50 for 2 months' wages, what is that a year? (300) What will 8 months' come to? (200) 16 months come to? (400) 12 years' come to? (450) 2 years' come to? (600) 10 years' come to? (3000) A. $4950.

15. What will 6 pieces of cloth, each piece containing 20 yards, come to, at $1,50 a yard? (180) What will 1 piece come to? (30) What will 3 pieces? (90) What will 5 pieces? (150) What will 10 pieces? (300) A. $750.

16. Bought 5 hhds. of rum, each containing 60 gallons, for $2 a gallon; what do they come to? (600) What will 4 hhds. come to? (480) What will 20 hhds.? (2400) A. $3480.

17. William's income is $1500 a year, and his daily expenses are $2,50; how much will he have saved at the year's end? A. $587,50. 18. If William's income had been $2000, how much would he have saved? (108750) If $2500 (158750) If $3600 ? (268750) If $4000 ? (308750) A. $8450.

19. If a hhd. of molasses cost $20,16, how much is it a gal lon? (Divide by the number of gallons in a hhd.) (32) How much is it a quart? (Divide by the number of quarts in a hhd.) (8) How much is it a pint? (4) How much is it a gill? (1)

A. 45 cents.

The foregoing questions have been solved by a method termed analysis This method is thought to accord with the natural operations of the human mind. Men in business scarcely recognise any other. The formality of state ments is rarely if ever made by them; and, when it is made, they do it more for the sake of testing the correctness of the other method, than for any practi

cal purpose. They may have adopted a statement in the commencement of their business, from the circumstance of having been taught it at school; but the longer they continue in business, the less occasion they have for it. Thero is another method, which consists in ascertaining the ratio or relation which one number has to another. This is used more or less by all, but more extensively by scientific men, and those well versed in mathematical principles.

20. If 8 pair of shoes cost 63 cents, what will 24 pair cost?

of 6373 cents, the price of 1 pair, which we multiply by 24 to get the price of 24 pair; thus, 24 × 7} = $1,89. But, since 7 is a fraction, it would be more convenient to multiply by 24 first, and divide by 8 afterwards, as this cannot make any difference; and, that we may make no mistake in the operation, we will make a statement, by writing the 63 cents on the right,

as a third term (see operation); on the left of which we write the multiplier, 24, as a 2d term, and, as a first term, the divisor, 8: then, 63 X 24 15128 $1,89, the Ans., as before.

=

Ans., $1,89

21. If 3 yards of cloth cost 24 cents, what will 6 yards cost

OPERATION.

yds.

yds. cts.

3

,

6 24

6

24 × 6=144÷÷3=48, the Ans OR, as we know that 6 yards cost 2 times as much as 3 yds., that is, =2, by simply multiplying 24 by 2, it makes 48, the answer, the same as before. This is a much shorter process; and, could we discover the principle, it would oftentimes render operations very simple and short In searching for this, we shall naturally to led to the consideration of ratio, or relation; that is, the relation which necessarily exists between two or more numbers.

3)144

Ans., $,48

RATIO. Q. What part of 6 is 5? A. §.

Q. What part of 5 is 6?

Q. What part of 3 is 4?

Q. What part of 4 is 3?

A. .

A..

A. 2.

Q. What is the finding what part one number is of another called? A. Finding the ratio, or relation of one number to another. What is ratio, then? A. The number of times one number, or quantity, is contained in another.