4 months; C put in $500 for 3 months. They gained $350. How must they share of this gain?

It is evident that $400 for 2 months is the same as $400 x2=$800 for one month.

And $300 for 4 months is the same as $300×4=$1200 for one month.

And $500 for 3 months is the same as $500 x3=$1500 for one month.

Hence, $800 A's money for one month.

1200 B's money for one month.

1500 C's money for one month.

Multiply each partner's stock by the time it was in trade; make each product the numerator of a fraction, and the sum of the products a common denominator; then multiply the whole gain or loss by each of these fractions, for each partner's share.

Repeat this Rule.

2. Three farmers hired a pasture for $55.50 for the season. A put in 6 cows for 3 months, B put in 8 cows for 2 months, C put in 10 cows for 4 months. What rent ought each to pay? A ought to pay $13.50.

Ans. B

12.00.

30.00.

3. On the first day of January, A began business with $650; on the first day of April following, he took B into partnership with 8500; on the first day of next July, they took in C with $450; at the end of the year they found they had gained $375. What share of the gain had each?

4. A, B and C, have together performed a piece of work for which they receive $94. A worked 12 days of 10 hours each; B worked 15 days of 6 hours each; C worked 9 days of 8 hours each. How ought the $94 to be divided between them?

A worked 12 × 10-120 hours.

5. A ship's company take a prize of $4440, which they agree to divide among them according to their pay and the time they have been on board. Now the officers and midshipmen have been on board 6 months, and the sailors 3 months; the officers have $12 per month, the midshipmen $8, and the sailors $6 per month; moreover, there are 4 officers, 12 midshipmen, and 100 sailors. What will each one's share be?

ASSESSMENT OF TAXES.

126. TAXES are moneys paid by the people for the support of government. They are assessed on the citizens in proportion to their property; except the poll tax, which is so much for each individual, without regard to

his property.

In order to ascertain what each individual ought to pay, an accurate inventory of all the taxable property must be made.

When a tax is to be assessed on property and polls, we must first see how much the polls amount to, which must be deducted from the whole sum to be raised; we must then apportion the remainder according to each individual's property.

To effect this apportionment, we find what per cent. of the whole property to be taxed, the sum to be raised is; we then multiply each one's inventory by this per cent., expressed in decimals, and the product is his tax.

Assessors find it convenient to form a table which shall at once give the taxes on small sums, from one dollar and upwards.

What are taxes? How are they assessed? What is a poll tax? Why must an accurate inventory of all the taxable property be made? When a certain tax is to be laid on property and polls, which must be found first? Having deducted the amount of poll taxes, how do we proceed? Having found the tax on one dollar, how do we obtain the tax for any other amount? May the labor be shortened by means of a table ?

EXAMPLES.

1. Suppose a tax of $600 is to be raised in a town containing 60 polls. If the whole taxable property amounts

to $37000, and each poll tax is $0.75, what will be A's tax, whose property is assessed at $653, and who pays one poll ?

$0.75 amount of one poll tax.

60

$45.00 amount of all the poll taxes.

$600 whole amount to be raised.

Deduct 45 amount of poll taxes.

$555 amount to be raised on $37000.

Hence, 55=$0.015 tax on one dollar.

37

Having found the tax on one dollar, we readily construct this

TABLE.

$1 pays $0.015 | $20 pays $0.30 | $200 pays $3 00

Now, to find A's tax, his property being $653, I find by

2. By the above table, what would be the tax on $425, there being no poll tax? Ans. $6.375. 3. By the same table, what must B pay, who has 2 polls, and whose real and personal property is assessed at $762? Ans. $12.93.

4. If C pays 3 polls, and is assessed at $1250, how much ought he to pay?

Ans. $21. 5. What is the tax on $375, there being no polls?

6. How much is the tax on $1875? 7. How much is the tax on $1100?

Ans. $5.625.

Ans. $28.125.

Ans. $16.50.

NOTE.-By this method school rates may be computed, taxes for building school-houses, or, indeed, rates for any other similar purposes.

EQUATION OF PAYMENTS.

127. EQUATION OF PAYMENTS is a process by which we ascertain the average time for the payment of several sums due at different times.

What is Equation of Payments?

Suppose I owe $1000, of which $100 is due in 2 months, $250 in 4 months, $350 in 6 months, and $300 in 9 months. Now, if I pay the whole sum at once, how many months credit ought I to have?

A credit on $100 for 2 months]

is the same as a credit on $1 for 100×2mo.=200mg, 200 months.