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months; and to F $500, payable in 4 years; now, what would be the equated time for paying the whole ? A. 223358 months

Questions on the foregoing. 1. A man bought a barrel of flour for 2£ 15 s. 6 d., a hhd. of molasses for £ 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 8,167 (1600) At $,124 ? (1200) `At $,64? (600) At $,5? (180) A. $14200.

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 31 d.

5. Reduce 7, 4, and $, to tie least common denominator. A. 18, 6. Change 2000 francs to federal money. A. $375 7. Toto +3 +1680 +673 +10oo00. A. 673,37505.

8. Change 4500£. English or sterling money, to dollars of 4s 6 d. cach. A. $20000.

9. What is the interest of $21,20 for 6 months ? (636). For 3 months 15 days ? (371) For 11 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 por cent., for 1 year? (321) At 3 per cent.? (309) At 5 per cent. ? (31650) At 9 per cent. ? (32925) At 124 per cent.? (33750) A. $1613,25

11. What is the discount of $315 for 10 months, at 6 per cant. ? (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. O no.? (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 grin, discounting at 6 per cent.? (Find the present worth of $488,75 first, then subtract lo 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 reinainder per gallon to lose nothing ? and how much to gain on the whole cost 20 per cent. ?

A. 30 ets.; and, to gain her ecat., 36 ets.

RULE OF THREE,

OR

SIMPLE PROPORTION. | LXXIII. 1. What will 3 yds. of cloth corne 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 marr ner 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? W: will 8 ? What will 12 ? What will 20 ?

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

5. If 20 yards of cloth cost 60 cents, how much is it a yari What will ( 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. vost 48 cents? How many will 24 cents buy? How many will 10 cents? How many will 108 cents ?

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

8. If you pay 16 cents for 4 oranges, how many cents wil bůy 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 ? callle over the winter, hop many tons will keep 6 cattle the same time? How many 8 How many 10? How many 20 ? How many 40 ? Hon many 60? How many 80 ?

11. If 500 cattle eat 1000 tons of hay in one winter, what will 2 cattle eat? What will 3? What will 5 ? What wi.. 20 ? What will 50 ? What will 200 ?

12. If 2 penknir es cost 25 cents, what will 3 cost? What will 4? VÝhat y,ill 8 ? What will 12: What will 16?

13. If you pay 26 cents for 2 inkstands, how many cents will

Will buy 4? 5? 6? 7? 8? 9? 10? buy 3 ?

20 ? 30?

40 ? 14. If of a yard of broadcloth cost 4 dollars, what will ccst? (if i cozt 4 dollars, š will cost 2 dollars.) What will f? What ģ? What } ? What ? What if? What if What 1 g ? What if? What if? What 18? What 2 yards What ? (If make 1 yard, then 1 yard and } are 3.) Wha! will be of a yard cost ? What ? What ar? What 16. What ?? What 3 yards?

15. The interest of 100 dollars for 1 year is C dollars at E per cent. ; what is it for 2 years ? F3:3? For 5 ? For 7? Fo: 9? For 12 ? For 20?

16. If 6 men can do a piece of work r. 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 vill 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 yurd is zo of $40 ; that is, 40 = 20 = $2 a yard; then, 8 yards are 8 X 2=$16, Ans.

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

3. If 2 bushels of oats cost 40 cenis, 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 ? (025) What wil 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 7 (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) Ilow much will $2,40 ? (16) A. 46 lbs.

10. If I pair of gloves cost 75 cents, what will 1 dozen pair cost ? (9) What will 14 doz. ? (1350) What will 2 doz.> (18) What will 24 doz. ? (2250) What will 3 doz. ? (27)

A. $90. 11. If 3 dcz puir of shoes cost 27 dollars, what will 1 pair cosi ? (75) What will 2% doz. ? (2250) What will 2 doz. 7 (18) What will 14 doz. ? (1350) What will 1 doz. ? (9)

.4. $63,75 12. If 5 tons of hay will keep 25 sheep over the winter, low many sheep can be kept on ĭ tons, at the same rate ? (35) 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 ycar ? (300) What will 8 months' come lo ? (200) 16 nonths' come to ? (400) 13 years' come to ? (450)

2 years' come to ? (600), 10 years' come to ? (3000) A. $4950.

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

16. Bought 5 bhds. of cum, each containing 60 gallons, for $2 a gallon; what do they come to ? (500) 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 aro $2,50 ; how much will he havo saved at the year's end ?

A. $587,50. 18. If William's income liad been $2000, how inuch would ho have saved ? (108750) If $2700? (158750) If $3600 ? (268750) If $4000 - (308750) 11. $8450.

19. If a lhd. of molasses cost. $20,16, how much is it a gal lon? (Divide by the number og gallons in a hhd.) (32) How much is it a quart? (Divide by the number of quarts in a hhd.) (3) 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 inind. Men in business carcely recognise any other. The formality of stato monts is rarely if ever maai by them; and, when it is made, they do it inosu for the sake of teeting the contactness of the other motlod, than for any practi

ca. purpose. They may have adopted a statement in tho coinmencement of neir business, frum ino 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 extop. sively by scientific men, and those well versed in nathematical principles.

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

} of 63 = 73 cents, the price of 1 pair, which we multip.'y by 24 to get the price of 24 pair ; thus, A X 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 niistake in the operation, we will make a statement, by writing the 63 cents on the right, OPERATION.

as a third term (see operation);

on the left of which we write the pair. pair. cents.

multiplier, 24, as a 21 term, and, as 8 24 63

a first term, the divisor, 8: then, 24 63 X 24 = 1512 ; 8= $1,89, the

Anz., as before.
252
126

8)1512 Ans., $ 1,89 2. If 3 yards of cloth cost 24 cents, what will 6 yards cost!

OPERATION. yds. yds. cts.

24 X 6=144:3=48, the Ans 3 6 24 Or, as we know that 6 yards cost 2

6 times as much as 3 yds., that is, of :2,

by simply multiplying 24 by 2, it makes 48, 3) 144

the answer, the same as befúre. This is a much shorter proccss; and, could we

discover the principle, it would oftentimes Ans., $,48 render operations very simple and short

In scarching for this, we shall naturally Im led to the consideration of ratio, or relation; that is, the relation which necessarily exists betwcen two or more numbers.

RATIO. Q. What part of 6 is 5 ? A. A.
Q. What part of 5 is 6? A.
Q. What part of 3 is 4? A. J.
Q. What part of 4 is 3 ?

ē. What is the finding what part one number is of another rulled? A. Finding the ratio, or relation of one nun.ber! another. What is ratio, then? A. The number of tir es otse sumber, o: quantity, is contained in another.

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