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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 $500; 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 ?

(A had $195. Ans. B 6 112:50.

1066 6750. 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 x10=120 hours.
B 66 15 x 6= 90 hours.
C 56 9x 8= 72 hours.

282
Therefore, A had Het of $94=i4 of $94=$40.

B had me of 94=# of 94= 30..

Chad 70 of 94=4 of 94= 24. 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 eacb one's share be?

(Each officer must have $120. Ans. < Each midshipman 66 80. (Each sailor

66 30.

1 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, 39550=$0·015 tax on one dollar. Having found the tax on one dollar, we readily construct this

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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 weing no polls ?

Ans. $5.625. 6. How much is the tax on $1875? Ans. $28.125. 7. How much is the tax on $1100? 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 7 is the same as a credit on $1 for 100 X 2mo.=200mo. 200 months.

A credit on $250 for 4 months is the same as a credit on $1 for 250 x 4mo.=1000mo. 1000 months.

A credit on $350 for 6 months is the same as a credit on $1 for 350 x 6mo.=2100mo. 2100 months.

A credit on $300 for 9 months is the same as a credit on $1 for 300 x 9mo.= 2700mo. 2700 months.

$1000 6000mo. Hence, I ought to have the same as a credit on $1 for 6000 months. But if I wish a credit on $1000 instead of $1, it ought evidently to be for only one thousandth part of 6000 months, which is 6 months.

Hence, we infer this

RULE.

Multiply each sum by the time that must elapse before is becomes due ; divide the amount of these products by the amount of the sums; the quotient will be the equated time.

EXAMPLES.

1. I purchased a bill of goods amounting to $1500, of which I am to pay $300 in 2 months, $500 in 4 months, and the balance in 6 months. What would be the mean. time for the payment of the whole ?

Ans. 4 * mo., or 4mo. 16da. 2. A merchant owes $500 to be paid in 6 months, $600 to be paid in 8 months, and $400 to be paid in 12 months, What is the equated time of payment ?

Ans. 8fmo., or 8mo. 12da.

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