2. What is the balance of the following account, and when is

it due?

Ans. Balance, $450; Due Jan. 23d.

3. What is the balance of the following account, and when is

it due?

Ans. Balance, $205; Due July 31st.

HENRY T. OSBORN.

Dr.

Cr.

4. The following account was settled by Mr. Kready giving his note for the balance; required the face of the note and the time when interest commenced.

Ans. Face, $475; Int. from March 8th.

5. What is the balance of the following account, and, if a

note is given, when does interest begin?

Dr.

1862

Ans. Balance, $900; Int. from Dec. 17, 1861.

SMITH, IN ACC'T WITH BRADFORD.

1862

$900 March 24, By Cash,

Cr.

$300

10da. $800

April 25, "Remittance, $300

May

April 20, " 4, "

66

$400 July 17, "Cash,

$200

66

$600

March 19, To invoice,

SETTLEMENT OF ACCOUNTS.

278. An Account Current is the statement of the mercantile transactions of one person with another.

379. Settling, or Closing an account, is finding how much is due to one of the parties at any specified time. Accounts Current are generally settled every six months or year.

380. In computing the settlement it is evident that interest should be allowed on each item in proportion to the time it is due before settlement. Such accounts are correctly settled by the following

RULE.-I. Find the time between each item coming due and the date of settlement, and compute the interest upon each item for the corresponding time.

II. Add the interest to the item if due before the date of settle ment, and subtract it when the item is due after the date of settle The difference of the sums of the results on both sides of

ment.

the account will be the cash balance.

1. Required the cash balance of the following account, July 16, 1862, interest at 6

per cent.

Ans. $200.60.

2. Required the cash balance of the following account, Aug. 8, interest 6 per cent.

Ans. $150.171.

SECTION X.

MEDIAL PROPORTION.

381. Medial Proportion, or Alligation, treats of mixing or combining two or more quantities.

382. The average value of a combination is called the Mean Value or Quality.

The subject is usually called Alligation, from the Latin alligo, to bind or unite together, a term suggested by the method of linking or uniting the figures with a line. The name is not very appropriate, as shown by its origin and the nature of the subject.

CASE I.

383. Given the quantity and value of each, to find the average value.

NOTE. This case is usually called Alligation Medial.

1. A merchant mixed 24lb. of sugar at 10ct. a pound, 30lb. at 14ct., and 261b. at 20ct.; what is the average price of the mixture?

SOLUTION.-241b. at 10ct. a pound cost 240ct., 301b. at 14ct. a pound cost 420ct., 261b. at 20ct. cost 520ct., and taking the sum we find 801b. cost 1180ct.; hence 1lb. cost of 1180ct., which is 14ct. From this solution we derive the following

OPERATION. lbs. cts. cts. 24 @ 10240 30 @ 14420 26 @ 20520

80 cost 1180

1 "80)118014, Ans.

RULE. Find the sum of the values of each ingredient, and divide it by the sum of the ingredients.

2. A person mixed 25lb. of tea at 50ct. a pound, 341b. at 80ct., and 41 at $1.10; what is the mean price or quality of the mixture? Ans. $0.844.

3. A drover bought 44 oxen at $40 each, 34 cows at $20 each, and 62 sheep at $5 each; what was the average value? Ans. $19.612.

4. A person mixed 18gal. of wine at $0.50, 20gal. at $0 80, 20gal. at $1.20, with 6gal. of water; what was the value of a gallon of the mixture? ̧ Ans. $0.769.

5. A smith combined 8oz. of gold 21 carats fine, 12oz. 22 carats fine, 18oz. 20 carats fine, with 28oz. of alloy; required the fineness of the composition.

6. A person mixed 12gal. of alcohol 90% strong, 10gal. 75% strong, and 11gal. 70% cent. of alcohol in the mixture?

Ans. 12 carats.

strong, 7gal. 80% strong; what per Ans. 79%.

7. A drover bought 30 cows at $20 a head, 40 at $25 a head, 30 at $28 a head; he sells them at a gain of 25%; what is the average price per head received? Ans. $30.50.

CASE II.

384. Given the mean value and value of each, to find the proportional quantity of each.

NOTE. This and the following case are usually called Alligation Alternate.

1. A grocer wishes to mix sugars worth 5, 7, 12, and 14 cents a pound, forming a mixture worth 9 cents a pound; in what proportion must the sugars be mixed?

SOLUTION. If we take 1lb. at 5 cents for the mixture, worth 9ct., we gain on it 4ct., and to gain lct.. we would take of a pound. If we take 1lb. at 14ct. we will lose 5ct., and to lose lct., what we have just

OPERATION. Ans.

5

gained, we would take lb.; hence we take 4lb. at 5ct. as often as 1b. at 14ct., or in whole numbers, 20 times, which is 5 of the first, as often as 20 times, which is 4 of the fourth. In a similar manner we find that we must take 31b. at 7ct. as often as 21b. at 12ct.; hence the quantities may be mixed in the proportion of 5, 3, 2, and 4.

་

RULE.-I. Select two quantities, one less the other greater than the average, subtract each from the average, and write the recip rocal of the difference opposite the quantities used, as the first couplet, and reduce these to integers by multiplying by the leasi common denominator.

II. Proceed in the same manner with the other quantities until all have been used, and the results will be the proportional quantities required.

NOTES.-I. When there are three quantities, compare the one which is greater or less than the average with both the others, and take the sum of the two numbers opposite this one.

II. A common factor may be inserted in any couplet or omitted from it without changing the proportional parts.

2. What relative quantities of wine worth 7, 10, 16, and 18 dimes a gallon must be taken to form a mixture worth 12 dimes a gallon? Ans. 6; 4; 2; 5. 3. How many pigs at $5, sheep at $8, cows at $20, and oxen at $30, must be taken to form a drove which shall average $18 Ans. 12 pigs; 2 sheep; 10 cows; 13 oxen.

per

head?

4. A merchant has 4 pieces of muslin, worth 10, 14, 20, and 22 cents a yard, respectively; how many yards must he sell from each that the price may average 18 cents?

Ans. 1st, 2; 2d, 2; 3d, 4; 4th, 4. 5. How shall I combine gold 16 carats, 18 carats, and 22 carats, to make a mixture of 20 carats fine, if I wish to mix equal quantities of 1st and 2d? Ans. 1st, 1; 2d, 1; 3d, 3.

6. What relative quantities of rice worth 121, 183, and 201 cents a pound, must be taken to form a mixture worth 161 cents a pound? Ans. 27; 15; 15.

SUG. Reduce to a common denominator, and compare the nume

rators.

7. A farmer bought pigs at $4 each, sheep at $51 each, and calves at $6 each; how many must he sell of each so that the Ans. 9; 2; 3. average price may be $5 each?

8. A man has a sum of money consisting of 3ct., 5ct., 25ct., and 50ct. pieces, which he wishes to exchange for 10ct. pieces; what is the relative number of pieces exchanged?

CASE III.

Ans. 40; 15; 5; 7.

385. Given the mean value, the value of each, and the quantity of one, to find the others.

1. A farmer bought 20 hens at 10 dimes each; how many must he buy at 4 and 5 dimes each, so that the average price may be 8 dimes each?