tity, we find their value, and also that of one of each of the others, the sum being the value of 20 pounds. The difference between this sum and 20 pounds at the mean rate is 8 cents; hence we see that the quantity of one or more of the lower priced ingredients must be increased without increasing those that are limited; it is desirable therefore that a whole number be added to the quantity which is to be increased, although a fraction will also give the correct proportion, hence we take the difference between the mean rate (20) and 16, which gives us 4 to divide into,8, the quotient being 2, which we add to the 1 pound at 16 cents making 3 pounds. 32. A tobacconist would mix 14 pounds of tobacco at 42 cents a pound, 24 pounds at 36 cents a pound, with two other kinds, one at 24 cents and the other at 18 cents a pound; how much of each of the two latter kinds must he take to make the mixture worth 30 cents a pound? Ans. 50 pounds at 24 cents, and one pound at 8 cents a pound; or 17 pounds of each of the latter kinds. 33. A brewer would mix 28 gallons of ale at 18 cents a gallon, and 18 gallons at 9 cents a gallon, with two other kinds, one at 16 cents, and the other at 12 cents a gallon; how much of the 16 and 12 cent ale must he take that the mixture may be worth 11 cents a gallon. Ans. 20 gallons of each. 34. I have 18 gallons of wine at 48 cents a gallon, 8 gallons at 52 cents, and 4 gallons at 85 cents, and would mix the whole with two other kinds of wine, one at $1.26 and the other at $2.12 a gallon; how much of the wine at $1.26, and of that at $2.12 must I mix with the other three that the mixture may be worth $1.00 a gallon? Ans. 10 gallons of each. 35. A lady purchased 14 yards of calico at 22 cents a yard, and 12 yards at 20 cents a yard; she wished to know how many yards of two other kinds, one at 15 cents, and the other at 17 cents a yard, she must purchase to make the average price of the whole 18 cents a yard? Ans. 20 yards of each of the other two kinds. EQUATION OF PAYMENTS. Equation of payments consists in finding a mean time for the payment at once of several debts, payable at different times, so that no loss of interest shall be sustained by either party. 1. A owes B $46 dollars, $12 of which is to be paid in 8 months, $16 in 5 months, and $18 in 3 months; at what time may the whole debt be paid at once, without injustice to either party? Explanation. The interest of $12, for 8 months, is the same as the interest of $1 for 96 months; the interest of $16 for 5 months is the same as that of $1 for 80 months; and the interest of $18 for 3 months is the same as that of $1 for 54 months; hence the interest of $12 for 8 months, of $16 for 5 months, and of $18 for 3 months is the same as the interest of $1 for 230 months, which is equal to the interest of $46 for 5 months; therefore 5 months is the medium time for the payment of the whole debt. From the above illustration we infer the following RULE. Multiply each payment by the time at which it is due, and divide the sum of the products by the sum of the payments, and the quotient will be the equated time. 2. E owes G $2400, of which $480 are to be paid at 5 months, $960 at 8 months, and the rest at 12 months; but they agree to make one payment of the whole; what is the equated time? Operation. 480 × 5 2400 960 × 8= 7680 2400 )21600(Ans. 9 months. 3. A owes B $380, of which $100 are to be paid in 6 months, $120 in 7 months, and $160 in 10 months, but they agree that the whole shall be paid at one time; when must it be paid? Ans. In 8 months. 4. A merchant sold goods amounting to $1500, to be paid as follows, $250 in 2 months, $500 in 5 months, and $750 in 8 months; what is the mean time of paying the whole? Ans. 6 months. 5. A merchant has due him $300, to be paid in 60 days, $500 to be paid in 120 days, and $750 to be paid in 120 days; what is the equated time for the payment of the whole? Ans. 108 days. 6. A owes B $640, $150 due in 30 days, $200 due in 60 days, and the remainder in 90 days; what is the equated time for the payment of the whole? Ans. 66 days. 7. C owes D the following sums, viz., $180 now due, $120 due in 3 months, $200 due in 6 months, and $300 due in 12 months, and they have agreed to make one payment of the whole; at what time must it be made? Ans. 62% months. 8. A merchant purchased goods to the amount of $2000, of which $400 are to be paid at present, $800 at 6 months, and the rest at 9 months; but it is agreed to make one payment of the whole; when must it be paid? Ans. 6 months. 9. G owes K $420, which will be due 6 months hence; it is agreed that $60 shall be paid now, and that the rest remain unpaid a longer time than 6 months; when must it be paid? Ans. In 7 months. REDUCTION OF CURRENCIES. Previous to the act of Congress establishing a mint, and regulating the coin of the United States, (in the year 1792,) each State had its own particular currency. Under the colonial government the several States issued bills of credit, to supply the want of specie, and to answer as a medium of trade; but as these bills were not received by the British merchants in payment for goods at their par value, holders of the bills had to pay more. Thus in New York they had to pay in bills of that State, at the rate of 8 shillings for 4s. 6d. sterling, (4s. 6d. sterling being taken as the value of a dollar.) In New England 6 shillings were taken as the value of a dollar. The following table shows the value of a dollar of this currency in the several States: New England, Virginia, Kentucky, and Tennessee, 6s.=$1. New York, North Carolina, and Ohio, Pennsylvania, New Jersey, Delaware, and Maryland, South Carolina and Georgia, 8s.=$1. 7s. 6d. $1. 4s. 8d.=$1. In Canada and Nova Scotia the dollar is valued at 5s. sterling, or English money, 4s. 6d.=$1. 1. Change £218 7s. 4d. New England currency to Federal money. Here we express the given sum in shillings, and since 6 shillings make a dollar, we place 6 on the left of the line, &c. 2. Change $727.888 to New England currency. 3. Change £46 16s. 6d. of the old currency of New York to Federal money. Ans. 117.06. 4. Change $117.064 to the old currency of New York. 5. Change £387 of the old currency of Pennsylvania to Federal money. Ans. $1032. 6. Change $1032 to the old currency of Pennsylvania. 7. Change £187 9s. 10d. of the old currency of Georgia to Federal money. Ans. $803.534. 8. Change 803.534 to the old currency of Georgia. 9. Change £25 10s. 6d. Canada currency to Federal money. Ans. $102.10. 10. Change $109.10 to Canada currency. NOTE. The comparative value of the dollar and the pound sterling, 、as given above, is called the nominal par value. The actual value of the pound is more than is here given. This difference is usually estimated in trade by adopting the nominal value as given above, as the basis of the calculation, and then adding or subtracting a certain per cent. to compensate for the inequality of value. In calculating ad valorum duties in the custom-houses of the United States, on goods imported from England, the pound sterling is estimated at $4.84, according to act of Congress, passed January 18, 1837. EXCHANGE. Exchange is the act of paying or receiving the money of one country for its equivalent in the money of another country, by means of bills of exchange. It comprehends both the reduction of money and the negotiation of bills. A bill of exchange is a written order for the payment of a certain sum of money, at an appointed time. It is a mercantile contract, in which four persons are generally concerned, viz. 1st. The drawer, who receives the value, and is also called the maker and seller of the bill. 2d. The person upon whom the bill is drawn is called the drawee. He is also called the acceptor, when he accepts the bill, which is an engagement to pay it when due. 3d. The person who gives value for the bill, is called the buyer, taker or remitter. 4th. The person to whom it is ordered to be paid, is called the payer, who may, by endorsement, pass it to any other person. |