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68 If E can do the same work in 7 days, how long would be required for C, D, and E, to do it working together?

Ans. 28 days.

69* If A, B, and C can do a piece of work in 6 days, and A and B can do the same work in 8 days, in what time can C do it alone? Ans. 24 days. 70* Shipped to Havre 2000 bbls. of flour, which I sold at $73 per bbl.; received in return 5003 hhds. of wine, worth $211 per hhd.; what sum is still due me?

71 A merchant owned & of a cargo of teas, the whole cargo worth $65000; he sells of his share for $8583.331; does le gain or lose, and how much?

-72. From a tank containing 184 gallons of water, 20 gallons were drawn out; if g of what then remained was equal to § of what afterwards rained in, how much rained in? How much did the tank then contain? Ans. 236 gallons.

73* I pay $700 for a piece of land; cut 52 cords of wood from it, which I sell at $5.40 a cord; I pay $1ğ a cord for cutting and hauling the wood, and $10 for surveying the land; I divide 3 acres of it into house lots of acre each; 4 of these I sell at $175 each, and the rest at $162.50 per lot. Reserving 2 acres for myself, valued at $300, I sell the remainder of the land for $600, what do I gain? Ans. $2388.183.

74 Messrs. B, D, W, and S, built a drain together, each agreeing to pay his proportion of whatever he occupied. B occupied 20 feet alone, B and D 22 feet, B, D, and W, 140 feet. B, D, W, and S, 18 feet. The drain was built at a cost of 331 cents per foot; what was each person's share of the cost?

NOTE. - B's share 20 × 33+ 22x33 +140X3318X331

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Ans. B, $27.38;; D, $20.72; W, $17.05§; S, $1.50. 75% A, B, C, and D, hired a team together in Boston for a journey north, each agreeing to share the expense for the distance he rode. At Reading, 14 miles from Boston, A got out; at Andover, 8 miles further, B got out; at Lawrence, 4 miles further, C left, and D went on alone 8 miles to Haverhill. Re

turning, he took up C, B, and A, where he left them, and all rode into Boston. They paid $8.50 for the use of the team; what was each one's share?

NOTE.—The distance from Boston to Haverhill is 34 miles; the price for 1 mile out and back is $8.50 = $.25; D's share is 1425+ 8×25 +4X25 +8 x 25.

Ans. A, $.87; B, $1.544; C, $2.04д; D, $4.04¿.

149. GENERAL REVIEW, No. 3.

1. What are the prime factors of 420? -- 3

2. Divide 15 X 7 X 12 × 8, by 21 × 10 × 3 × 4. — 3. What is the greatest common divisor of 21, 84, and 51? 4. What is the least common multiple of 42, 9, 14, and 12? 5. Reduce and to their lowest terms. 56

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6. Reduce 254 to an improper fraction. !!! 2

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7. Reduce 688 to a mixed number. ¡7

8. Reduce of 4 of 2 of 65 to a simple fraction.

9. Reduce 3, 3, and §, to a common denominator.

10. Reduce 1, 14, and 8%, to the least common denominator. 11. Add † of 4, 14, and 94. //

12. Add 15, 3, and 253. 43

13. From of take 1.

14. Subtract 81 from 10.

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19. What is the greatest common divisor of,, and 23? 20. What is the least common multiple of,, and ? 21. How many fourths of§ of 40 in 34 × ÷ of 9?

For changes, see Key.

7

COMPOUND DENOMINATE NUMBERS.

150. Numbers are either Simple or Compound.

151. A Simple Number is a number expressed in units of one denomination; as, 5 books, 7 pens.

152. A Compound Number is a number expressed in units of two or more denominations, but of the same nature; as, 5 pounds 6 ounces of sugar, 3 years 2 months 4 days of time.

153. Reduction is the process of changing the denomination of numbers without altering their value.

154. Reduction Descending is the process of changing numbers to numbers of equal value in lower denominations; thus, 1 dollar 100 cents.

155. Reduction Ascending is the process of changing numbers to numbers of equal value in higher denominations; thus, 100 cents = 1 dollar.

156. Compound numbers express Currency, Weight, and Measure.

CURRENCY.

Every nation has its own currency.

That of the United

States has already been given (Art. 68), but the table will be inserted here for the sake of uniformity.

157. FEDERAL MONEY.

The denominations are eagles, dollars, dimes, cents, and mills. The legal coins in circulation are as follows:

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copper and silver

NOTE. The gold coin is hardened by an alloy of (the silver not to exceed the copper). The silver coin is hardened by copper. The cent coined since 1856 has 88 parts of copper to 12 of nickel. The two-cent piece, coined 1864, has 95 parts copper to 5 of tin and zinc. TABLE.

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NOTE.-Mill is derived from the Latin mille, one thousand, because 1000 mills 1 dollar, the unit of computation; cent from Latin centum, one hundred, because 100 cents 1 dollar; dime from the French dîme,

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a tenth, as a dime is one tenth of a dollar; dollar from the German thaler, dollar, dollars having been first coined in Germany.

EXERCISES.

1. Write 3 E. $2. 7 d. 5 c. 2 m. as it is usually written.

Ans. $32.752.

Ans. $1628.398.

2. Write 162 E. $8. 3 d. 9 c. 8 m. as it is usually written.

3. 128 E. 3 d. 8 m.

Write in the same manner,

4. 19 E. $6. 3 c. 2 m.

5. 68 E. $8. 2 m.

6. $7.2 c. 5 m.

7. $5. 6 d. 8 c.. 3 m.

8. 3984 E. 7 d. 4 c. 8 m.

9. Add the answers of the last six examples, and give the amount in mills.

Ans. 42,017,798 mills

158. ENGLISH MONEY.

The denominations are pounds, shillings, pence, and farthings.

TABLE.

4 farthings (qr. or far.) 1 penny, marked d.

12 d.

20 s.

NOTE.

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The guinea of 21 s., and the crown of 5 s., are also used. Th

soin which represents the £ value is called a sovereign.

159. REDUCTION DESCENnding.

ILL. EX. Reduce 3£ 11 s. 8 d. 2 far. to farthings.

OPERATION.

3 £ 11 s. 8 d. 2 far.

20

71 s.

12

860 d.

4

3442 farthings, Ans.

60 s.;

1 s., we

As 20 s. 1 £, we shall have 20 times as many s. as £. (20 × 3) s. 60 s. 11 s. 71 s. As 12 d. shall have 12 times as many d. as s.; (12 × 71) d. 852 d. ; 852 d. + 8 d. 860 d. As 4 far. = 1 d., we shall have 4 times as many far. as d.; (4 × 860) far. = 3440 far; 3440 far. +2 far. 3442 farthings. Hence the

RULE FOR REDUCTION DESCENDING. Multiply the number of the highest denomination by the number which it takes of the next lower denomination to make one of that higher, and to the product add the given number of the next lower denomination. Multiply that sum in like manner, and thus proceed till the number is reduced to the required denomination.

EXAMPLES.

1. Reduce 7 £ 8 s. 3 d. 3 far. to farthings. 2. Reduce 30 £ 2 s. 0 d. 2 far. to farthings.

3. Reduce 8 £0 s. 3 d. to farthings.

4. Reduce 9 s. 1 d. 2 far. to farthings.

5. Reduce 368 £ 17 s. 2 d. to pence.

6. Reduce 25 crowns 3 s. 2 d. to farthings. 7. Reduce 43 crowns 4 s. 8 d. to pence.

8. Reduce 209 guineas to pence.

Ans. 7119 far.

Ans. 28898 far.

9. What will be the number of farthing candles that may be bought for 2 s. 6 d.?

160. REDUCTION ASCENDING.

ILL. EX. Reduce 3579 farthings to an equivalent value in higher denominations.

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