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161. Bought sugar at 11 ct., and sold it for 11 ct.; what rate per cent. did I lose?

162. My agent purchased flour for me, which, with his commission of 21%, cost $4,130; I sold it at an advance of 25% on the buying price. What did I make, if the storage cost $13.20, and the insurance % of the buying price?

163. A broker buys stock, at 20% discount, and sells it at 16% discount; what is the rate per cent. of his gain? 164. A man buys stock at 12% discount, and sells it at 10% premium; what is the rate per cent. of gain?

165. I bought coffee at 30 ct.; what must be the marking price that will allow a discount of 25 % and still give me a profit of 20% on purchase price?

REVIEW.-What is the meaning of per cent.? (177.) How many parts are there in the problems of percentage? (178.) Define base. (179.) Rate. (180.) Percentage. (181.) Amount. (182.) Difference. (183.) What is Prob. L.? (183., a.) Give each of the problems in percentage. (183.) Define agent. (184.) Commission. (185.) Brokerage. (186.) A firm. (187.) A charter. (188.) A corporation. (189.) Capital. (190.) Stock. A share. (191.) What are stockholders? (192.) When is stock at par? (193.) Above par? (194.) Below par? (195.) What is the market value of stock? (196.) What is a dividend? (197.) Define profit. (202.) Loss. Gain. What is insurance? (207.) Define insurer. (208.) Who are the insured? (209.) Define policy. (210.) Premium. (211.) What are taxes? (213.) What is a specific tax? (214.) An ad valorem tax? (216.) Real estate? (217.) Personal property? (218.) Schedule? (219.) What is interest? (220.) Define principal. (222.) Rate. (223.) Amount. (224.) Simple interest. (225.) Compound interest. (226.) Legal interest. (227.) Define partial payment. (232.) Indorsement. (233.) Repeat the Supreme Court rule. (233., a.) What is a bank? (238.) Define bank discount. (239.) A promissory note. (240.) Bank notes. (241.) What are days of grace? (242) What is the maturity of a note? (243.) What are the proceeds of a note? (244.) Define exchange. (247.) Bill of exchange. (248.) Drawer. (249.) Maker. Drawee. (250.) Payce. (251.) Buyer. (252.) Remitter. Acceptance. (253.) Indorsement. (254.) A domestic bill. (255.) A foreign bill. (256.) What is the course of exchange? (257. When 1s exchange at par? (258.) Above par? (259.) Below par? (260.) What is a partnorship? (262.) Who are partners? (263.) What is capital? (264.) What is a dividend? (265.) What is an assessment?

SECTION XII.

LESSON I.

ALLIGATION.

268. Alligation Medial is the process of finding the mean price or quality of a mixture, when the quantity of each ingredient and its price or quality are known.

A wine merchant mixes 12 gallons of wine worth $1.50 per gallon, and 9 gallons of brandy worth $2 per gallon, with 5 gallons of water; what is the value of the mixture?

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FORM.-1. Since 12 gallons of wine at $1.50 per gal. are worth $18, and 9 gallons of brandy at $2 are worth $18, and 5 gallons of water are worth nothing, the whole 26 gallons will be worth the sum of $18 and $18, which is $36.

2. If 26 gallons of the mixture are worth $36, one gallon is worth of $36, which is $1.38.

(a.) Rule.-Divide the entire cost of the given simples by the entire quantity; the result will be the mean price.

1. A grocer mixed 13 gallons of water with 40 gallons of brandy, worth $1.25 per gallon; will he gain or lose, by selling the mixture at 5 cents per gill?

2. A grocer mixed together 25 lb. coffee worth 50 ct. per lb. and 16 lb. of chiccory worth 15 ct.; what are 3 lb. of the mixture worth?

3. A grocer mixed together 54 lb. of tea at $1.25 per lb., and 2 lb. at $.75, and 2 lb. at $.60; how much is 1 lb. of the mixture worth?

4. A milkman bought milk at 10 ct. per qt.; he makes it one-fifth water; for how much per quart ought he to sell the mixture so as to make 50% on cost?

5. A grocer mixed 120 lb. of sugar at 5 ct. a pound, 150 lb. at 6 ct., and 130 lb. at 10 ct.; what is the value of the mixture per pound?

6. I mix alcohol of 100%; of 80 %; of 50%; of 331 %; what is the strength of the mixture?

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269. Alligation Alternate is the process of finding what quantity of simples whose prices or qualities are given, must be taken to make a mixture of any given price or quality.

270. To find what quantity of each simple must be taken to form a mixture of a given value.

I have different qualities of sugar, worth respectively 10, 11, 12, 14, and 15 ct. per lb.; what proportion of each must I take to make a mixture worth 13 cents?

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NOTE.-For convenience the gain is marked +, and the loss is marked sum of the 1st and a make b. Three times a make c, etc. In the same manner any number of proportional quantities may be found; hence every problem can have an indefinite number of answers.

FORM.-1. For convenience arrange the prices of the simples in a column, in the order of their values, with the given mean at the left.

2. By using 1 lb. of sugar at 10 cts. in a mixture to be sold at 13 cts., the gain is 3 cts.; by using 1 lb. at 11 cts., the gain is 2 cts.; by using 1 lb. at 12 cts. the gain is 1 ct.

3. By using 1 lb. sugar at 14 cts. in a mixture to be sold at 13 cts., the loss is 1 ct.; by using 1 lb. at 15 cts., the loss is 2 cts.

4. Since the gain on each quantity used in the mixture must equal the loss on some other quantity used, hence 1 lb. of sugar at 10 cts. should be used with 3 lb. at 14 cts., which write in the 1st column; and 2 lb. at 10 cts., with 3 lb. at 15 cts., which write in the 2d column; and 1 lb. at 11 cts. with 2 lb. at 14 cts., which write in the 3d column; and 1 lb. at 11 cts. with 1 lb. at 15 cts.; and 1 lb. at 12 cts., with 1 lb. at 14 ets.; and 2 lb. at 12 cts. with 1 lb. at 15 cts.

5. Thus the proportional quantities (column a.) in a mixture of 19 lb. are 3 lb. at 10 cts.; 2 lb. at 11 cts.; 3 lb. at 12 cts.; 6 lb. at 14 cts., and 5 lb. at 15 cts.

(a.) When the quantity of the mixture is limited.

FORM.-1. If two or more quantities are proportional, any multiple of those quantities are proportional.

2. Thus to produce a mixture containing 25 lb., add 23 lb. of b. with 2 lb. of the 4th proportional.

3. To produce a mixture containing 100 lb., take 5 times a. plus 5 lb. of the 2d, etc.

(b.) When one or more of the simples is limited.

FORM.-1. To make a mixture containing 69 lb., which shall contain 7 lb. of the 15 ct. sugar, add 19 lb. of a., 6 lb. of the 6th with 44 ib. of the 5th, which will give the proportional quantities as follows: 3 lb. at 10 cts.; 2 lb. ‹ at 11 cts.; 29 lb. at 12 cts.; 28 lb. at 14 cts., and 7 lb. at 15 cts.

Rule.-I. Arrange the prices or qualities in the usual form.

II. Find the loss or gain on each simple, which arrange in a column opposite.

III. Make a proportion of each simple above the mean with each simple below the mean, so that each loss will equal the gain, which write in separate columns.

IV. Arrange columns of proportional quantities at option, by adding the total proportional quantities to any of the preceding columns, or by multiply, ing it by any number.

7. A gentleman owns 4 pieces of land, worth $50, $65, $73 and $90 respectively. How many acres must he sell from the different tracts to realize an average price of $75.25

an acre?

8. A merchant has 3 pieces of cloth, worth respectively $.65, $1.25 and $1.85 per yd. How many yards must he sell from the three pieces to realize an average price of $1.50 per yd.?

9. In what proportions must we take coffee at 20 cts., 35 cts., and 50 cts., to form a mixture worth 40 cts. per lb. ? *

SECTION XIII.

LESSON I.

RATIO.

271. Ratio is the number of times one number is contained in another of the same kind.

272. The Terms of a ratio are antecedent and consequent, and taken together they are called a couplet.

273. The Antecedent is the first term of the couplet, and is the standard of measure, or the divisor, by which the other number is divided.

274. The Consequent is the second term of the couplet, and is the number measured, or the dividend.

275. Ratio may be expressed in two ways:

1. By two dots between the terms of the couplet; as, 3:12.

2. In the form of a fraction, as, 12, or 12 divided by 3.

(a.) NOTE.-All numbers are finally compared with unity as a standard; hence, when we say that the ratio 4: 8 is 2, it is understood that the ratio 4: 8 is equal to the ratio 1:2; and the ratio 4: 3 is ; or 4: 3 is the same ratio as 1 : 4.

What part of 12 is 4?

MENTAL EXERCISES.

ILLUSTRATION.-4 is of 12; or the ratio 12: 4==; that is, 12 has the same ratio to 4 that 1 has to

1. What part of 20 is 2? 5? 7? 8? 6? 9?

2. What part of 2 is 3? 9? 24? 30?

3. What part of 2 is 1? 2? 8? 4?

4. What is the ratio of 6 to 7?

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