2. A, B, and C send a ship to sea, which together with her cargo was worth $15000. A and B owned each onefifth, and C the rest. They gained $1250: how much did each pay towards the ship and cargo, and what did each receive of the profits? 3. A man bequeathed his estate to his four sons in the following manner, viz: to his first $5000; to his second $4500; to his third $4500; and to his fourth $4000. But on settling his estate it was found that after paying debts, charges, &c. only $12000 remained to be divided: how much must each receive? Ans. Sfirst son $3333,33; second $3000; third $3000; fourth $2666,663. 4. A widow and her two sons have a legacy of $1500, of which the widow is to have one-half and the son's each one-fourth. Now suppose the eldest son to relinquish his share, and the whole to be divided in the above proportions between the mother and younger son, what will each receive? 5. Suppose premiums to the value of $12 are to be distributed in a school in the following manner. The premiums are divided into three grades. The value of a premium of the first grade is twice the value of one of the second; and the value of one of the second grade twice that of the third. Now there are 6 to receive premiums of the first grade, 12 of the second, and 6 of the third: what will be the value of a single premium of each grade? (1st grade $0,888. Ans. 2d 66 $0,444. 6. Four traders form a company: A puts in $400 for 5 months; B $600 for 7 months; C $960 for 8 months; D $1200 for 9 months. In the course of trade they lost $750: how much falls to the share of each? 7. A and B lay out certain sums in merchandise amounting to $320, of which A pays $180 and B $140; they gain by the purchase $64: what is each one's share? Ans. A's $36; B's $28. TAXING. A tax is a sum required to be paid to the government for its support. It is generally collected from each individual in proportion to his property. In some states, however, every white male citizen over the age of twenty-one years is required to pay a certain tax. This tax is called a poll tax; and each person so taxed is called a poll. In assessing taxes, the first thing to be done is to make a complete inventory of all the property in the town on which the tax is to be laid. If there is a poll tax, make a full list of the polls, and multiply the number by the tax on each poll, and subtract the product from the whole tax to be raised by the town; the remainder will be the amount to be raised on the property. Having done this divide the whole tax to be raised by the amount of taxable property and the quotient will be the tax on $1. Then, multiply this quotient by the inventory of each individual, and the product will be the tax on his property. A certain town is to be taxed $4280, the property on which the tax is to be levied is valued at $1000000. Now there are 200 polls, each taxed $1,40. The property of A is valued at $2800, and he pays 4 polls, B's at $2400 pays 4 polls, C's at $2530 pays 2 D's at $2250 pays 6 What will be the tax on one tax. Also the tax on each? 66 66 E's at $7242 pays 4 polls, F's at $1651 pays 6 66 G's at $1600,80 pays 4. dollar, and what will be A's $1,40×200=$280 amount of poll tax. $4280-$280-$4000 amount to be levied on property. $4000 $1000000=4 mills on $1. Then, to find the tax of each, as A's for example. A's inventory 4 polls at $1,40 each A's whole tax $2800 ,004 11,20 5,60 $16,80 In the same manner the tax of each person in the town ship may be found. The assessors after finding the per cent., or the amount to be raised on each dollar, often form a table showing the amount which certain sums would produce. Thus, after having found, as in the last example, that 4 mills is to be raised on each dollar, we can, by multiplying by the several numbers 1, 2, 3, 4, obtain the following table. 1. Find the amount of B's tax from this table. 2. Find the amount of C's tax from the tables. In a similar manner we might find the taxes to be paid by D, E, &c. EQUATION OF PAYMENTS. In finding the equated time of payments, for several sums due at different times, any day may be assumed as the one from which we reckon. Thus, if I owe Mr. Wilson $100 to be paid on the 15th of July, $200 on the 15th of August, and $300 on the ninth of September, and we require the mean time of a single payment, it would be most convenient to estimate from the first of July. From 1st of July to 1st payment 15 days to 2nd payment 45 days Hence, the amount will fall due in 52 days from the 1st of July: that is, on the 22nd day of August. But we may, if we please, demand at what time the payment would be due from the first of June. From June 1st to 1st payment 45 days "2nd payment 75 days Hence the payment becomes due in 821 days from June 1st, or on the 22nd of August-the same as before. Any day may, therefore be taken as the one from which the mean time is estimated, Ex. 1. Mr. Jones purchased of Mr. Wilson, on a credit of six months, goods to the following amounts, 15th of January, a bill of $1250. 10th of February, a bill of 1000. He wishes, on the 1st of July, to give his note for the amount; at what time must it be made payable. Ans. Sept. 1. Ex. 2. Mr. Jones bought $2000 worth of goods: he was to pay $800 in five months, $600 in six months, and the remainder in eight months; what will be the time of credit, if he pays the whole amount at a single payment? Ans. 6 mo. 6 days. Ex. 3. A owes B $200, of which $40 is to be paid in 3 months, $60 in 5 months, and the remainder in 10 months; what is the mean time of payment? Ans. 7 mos. 3 days. Ex. 4. Bought several lots of goods, as follows: A bill of $650, June 6th, Do. of 7940, August 1st. Now if the credit is 6 months, at what time will the whole become due? Ans. Jan. 24th. Ex. 5. Bought goods to the amount of $1280, to be paid for as follows, viz.: one-fourth in cash, one-fourth in 6 months, one-fourth in 7 months, and the remainder in one year; what is the average time of payment? Ans. 8 mo. 10 days. Ex. 6. Mr. Johnson sold, on a credit of 4 months, the following bills of goods, |