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PARTNERSHIP.

261. Partnership is separated into simple and compound. In simple partnership the capital of each partner is invested for the same time. In compound partnership the time for which the capital of each partner is invested is taken into account, as well as the amount of the capital; and the division of profits and losses is made proportionally to the amount of the capital and the time it is invested.

A and B enter into partnership. A puts in $2000 for 2 yrs., and B puts in $3000 for 1 yr. Their profits are $1400. What is the share of each?

The use of $2000 for 2 yrs. is equivalent to 2× $2000 for 1 yr. Hence their profits must be divided in the ratio $4000 to $3000; that is, 4: 3.

Ex. 158.

1. Three drovers rent a field of 9 A., at $5 an acre. A puts in 6 cows for 2 mos; B, 9 cows for 1 mo.; and C, 12 cows for 2 mos. How much should each pay? 2. In a co-partnership A contributed $400 for 9 mos.; B, $350 for 8 mos.; and C, $600 for 2 mos. Divide a gain of $570 among them.

3. At the end of 12 mos. A, B, and C, having a joint capital of $6000, find they have lost $625. A's capital of $2500 has been in the business for 12 mos., B's of $1500 for 8 mos., and C's of $2000 for 4 mos. Divide the loss among them.

4. A and B enter into partnership, A with $1800, and B with $900. At the end of 8 mos. B adds $300 to his capital. Divide a profit of $840 between them, at the end of the year.

AVERAGES.

262. If a dozen eggs weigh 1 lb. 8 oz., what is their average weight?

Since the 12 eggs weigh 1 lb. 8 oz., that is, 24 oz.,

the average

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1. A merchant mixes 3 lbs. of coffee worth 27 cts. a pound, 2 lbs. worth 35 cts., and 1 lb. worth 41 cts. What is the mixture worth a pound?

2. What is the cost of a gallon of a mixture containing 7 gals. worth $1.35 a gallon, 5 gals. worth $1.05 a gallon, and water enough to make the whole mixture 15 gals.?

3. Of 32 candidates for office, 3 were 20 yrs. old, 4 were 21, 12 were 22, 12 were 23, and 1, 24. What was

the average age of the candidates ?

4. A bankrupt owes A $962.50, B, $3487, and C, $12,686.50. His estate, after paying expenses of settlement, is $3427.20. How much can he pay on a dollar?

5. A grocer buys 106 lbs. of tea, at 80 cts. per pound, 75 lbs., at $1.24 per pound, and 94 lbs., at $1.30 per pound, and mixes the three lots together. At what price per pound must he sell the mixture so as to make 10% on his outlay?

6. In what proportions must oils worth $1.25 a gallon and 80 cts. a gallon be mixed to make a mixture worth $1.00 a gallon?

HINT. The loss on the $1.25 oil is 25 cts. a gallon. The gain on the 80 ct. oil is 20 cts. a gallon. Therefore there must be more of the 80 ct. oil taken than of the $1.25 oil, and in the ratio of 25: 20 or 5: 4.

7. In what proportion must oils worth $1.20 and 60 cts. a gallon be mixed, so that the mixture may be worth 70 cts. a gallon?

8. Solder is composed of tin and lead. If a solder weighs 10.44 times as much as an equal bulk of water, while tin weighs 7.29, and lead 11.35 as much, find the weight of each metal in a pound of solder.

AVERAGE OF PAYMENTS.

A has given to B notes as follows: $250, due in 3 mos. ; $400, due in 6 mos.; $700, due in 8 mos. He wishes to pay them all at one time. In how many months shall the entire payment be made?

The use of
The use of

The use of

$250 for 3 mos. equals the use of $750 for 1 mo.
$400 for 6 mos. equals the use of $2400 for 1 mo.
$700 for 8 mos. equals the use of $5600 for 1 mo.
$1350
$8750 for 1 mo.

The question is, for how many months is the use of $1350 equal to the use of $8750 for 1 mo.?

The answer required is 3 mos.

612 mos.

613 mos. Ans.

9. Find the equated time for the payment of $300 due in 3 mos., $500 due in 6 mos., $200 due in 9 mos.

10. A owes B $50 payable in 6 mos.,

mos., and $90 payable in 4 mos.

time of payment.

$60 payable in 8

Find the equated

11. A owes B $1000, payable at the end of 9 mos.

He

pays $200 at the end of 3 mos. and $300 at the end When is the balance due?

of 8 mos.

12. On the first day of January, A purchases of B $200

worth of goods on 3 mos. credit, and $500 worth on

4 mos. credit, and gives one note in payment. When does the note become due?

CHAPTER XIII.

POWERS AND ROOTS.

263. The square of a number is the product of two factors, each equal to this number.

are

Thus the squares of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

264. The square root of a number is one of the two equal factors of the number.

are

Thus the square roots of 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

265. The square root of a number is indicated by the radical sign, or by the fractional exponent

above and to the right of the number.

written

[blocks in formation]

267. Hence, since every number consisting of two or more figures may be regarded as composed of tens and units,

The square of a number will contain the square of the tens + twice the tens × the units + the square of the units.

SQUARE ROOT.

268. The first step in extracting the square root of a number is to mark off the figures in periods.

Since 112, 100 = 102, 10,000 = 1002, and so on, it is evident that the square root of any number between 1 and 100 lies between 1 and 10; of any number between 100 and 10,000 lies between 10 and 100. In other words, the square root of any number expressed by one or two figures is a number of one figure; of any number expressed by three or four figures is a number of two figures, and so on.

If, therefore, an integral number be divided into periods of two figures each, from the right to the left, the number of figures in the root will be equal to the number of periods. The last period at the left may consist of only one figure.

Find the square root of 1225.

12 25 (35 9

65)3,25 3 25

The first period, 12, contains the square of the tens' number of the root.

The greatest square in 12 is 9, and the square root of 9 is 3. Hence 3 is the tens' figure of the root.

The square of the tens is subtracted, and the remainder, contains twice the tens the units + the square of the units. Twice the 3 tens is 6 tens, and 6 tens is contained in the 32 tens of the remainder 5 times. Hence 5 is the units' figure of the root. Since twice the tens X the units + the square of the units is equal to (twice the tens + the units) x the units, the 5 units are annexed to the 6 tens, and the result, 65, is multiplied by 5.

269. The same method will apply to numbers of more than two periods, by considering the part of the root already found as so many tens with respect to the next figure.

Extract the square 7 89 04 81 (2809

4

48)3 89
3 84
5609) 5 04 81

5 04 81

root of 7890481.

When the third period, 04, is brought down, and the divisor, 56, formed, the next figure of the root is 0, because 56 is not contained in 50. The 0 is then placed both in the root and the divisor, and the next two figures, 81, are brought down.

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