5. What is the value in Paris of $5000 in New York, exchange $4.85 £1, and £125.20 francs?

6. What sum in New York will pay 2597937 francs in Paris, exchange as in 5th?

7. What is the value in Hamburg of $5000 in New York, when $4.80 = £1, £1 = 25.20 francs, and 1.80 francs = 1 mark banco?

7

1250 28

5

$5000 × 252 × 1 = 1250x7x5 = 145834 mark banco.

8. What sum in New York will pay 14583 mark banco in Hamburg, exchange as above?

14583 x 18 x 48 $5000.

= 252

9. What debt in St. Petersburg will $5000 in New York pay, when $4.80 £1 in London, £125.20f. in

Paris, 4f. 1 thaler in Dantzic, and 1 thaler = 2.60 roubles?

These problems may be solved by compound equations and ratios.

10. What sum in New York will pay 17062 roubles in St. Petersburg, exchange as above?

REM.—This circuitous system of Foreign Exchange has led us into the same thing in our own country when it is found to be advantageous; thus,

11. A merchant in St. Louis has a bill of $5000 to pay in New York; in St. Louis a draft on New York costs 11% premium, whilst New Orleans funds can be bought at 1% premium, and at New Orleans Havana funds are 1% discount; and at Havana, New York funds are at a discount of 14%. What sum in St. Louis will pay the bill by the direct and by the circuitous. method?

Direct,

25 ΧΟΥ, $5000 × 100

203
× 28 = $5075.

25

79 395

81

405

And $5000 × 215 × 188 × 1 = $4974.2217.

12. What is $4974.2217 in St. Louis worth in New York by the circuitous method?

4974.2211 × 489 × 199 × 188 = $5000.

I have not given a table of foreign values, as they are not permanent. The principle is the same in all cases.

REM. 1.—In the ratios, see that the decimals in the numerator and denominator are equal, and then they are like quantities and can be used as such.

103 100,

REM. 2.—When any thing is purchased at a premium, the ratio of the cost is increasing; as, at 3% premium, the ratio is 188; if purchased at a discount the ratio of the cost is diminishing; as, at 3% discount, the ratio is; hence, if I purchase a draft for $100 at 3% premium, the cost is $100 × 108 $103; and if I purchase a draft for $100 at 3% discount, the cost is $100 × 1% = $97.

=

COR. 1. The cost of a draft, when at a premium, is its face multiplied by an increasing ratio whose denominator is 100 and numerator 100 increased by the premium.

COR. 2.-When there is a discount, the cost of a draft is its face multiplied by a diminishing ratio whose denominator is 100 and numerator 100 diminished by the discount.

REM.-Reckoning by the old par value, £1 is equal 40 dollars, and $1 equal £. The par value of £1 is now fixed by Act of Congress at $4.8665.

ALLIGATION.

Alligation is the mixing of different qualities of grain, groceries, liquors, etc., in order to get an article of a certain price; thus, sugar at 5 cts. and 9 cts. per lb. may be mixed together in such proportions as to make an article of any value between the two given prices.

COR.-The mixture cannot be made of less value than 5 cts. nor more than 9 cts.; for if a quantity be taken at 5 cts., and some of 9 cts. be added, it will increase the value above 5 cts.; and if 5 ct. sugar be added to the 9 ct., it will diminish the value.

REM.-If both kinds are either above or below the required price, the mixture cannot be made

PROBLEM.

1. What relative quantity of each must be taken of two kinds of sugar, the one worth 5 cts. per lb., and the other 11 cts., in order that the mixture be worth 7 cts. per lb. ?

EXEMPLIFICATION.-For every lb. at 5 cts. there is a gain of 2 cts., and for lb. a gain of 1 ct.; for every lb. at 11 cts. there is a loss of 4 cts., and of 1 lb. the loss is 1 ct.; hence, if 1⁄2 lb. at 5 cts. be taken, and 4 lb. at 11 cts., the gain and loss will be equal; this is then the ratio; or, reducing the fractions to a common denominator and canceling the denominators, the ratio is 2 at 5 to 1 at 11.

REM.-It matters not how many different qualities are to be mixed, only two at a time can be mixed; .. the principle developed in the above problem is the only principle in alligation.

2. Mix together coffee worth 17 cts., 19 cts., 21 cts., and 24 cts., so that the mixture shall be worth 20 cts.

It is evident that 17 and 19 cannot make a mixture worth as much as 20 cents; it is also evident that 21 and 24 cannot make a mixture worth as little as 20 cts.; but 17 and 21, 19 and 24, 17 and 24, and 19 and 21 may be mixed so as to be worth 20 cts.

By the first is taken 1 at 17 to 3 at 21; and 4 at 19 to 1 at 24; again, 4 at 17 to 3 at 24; and 1 at 19 to 1 at 21. All the mixtures being of the same value, may be put together, and the whole will be worth 20 cts.; thus,