:: 31 mo. 3. If 120 bushels of oats will 10. A man lent $350 to reserve 14 horses 56 days, how ceive interest, and when it had many days will 94 bushels serve continued 9 months, he received, 6 horses? principal and interest together, Ans. 10215 days. $360.50; at what rate per cent did he lend his money? 4. If $100 gain 86 in 12 mo. Ans. 4 per cent. what will be the interest of 8350 for 2 years and 7 months ? 11. With how many pounds $ mo. sterling could I gain £5 per an2y.7m0.3lmo. 100:6:: 350 num, if with £450 I gain in 16 12: months, 530? Ans. 100. Ans. $54.25. 12. If 1 lb. of thread make 3 5. If a sum of money at 6 per yards of linen 5 qrs. broad, how cent, simple interest, double in many pounds of thread will be 200 months, what will be the in wanted to make a piece of linen terest of $300 for 8 months ? 45 yards long and i yard broad? $ $ Ans. 12 lb. 100 : 100 :: 300* Ans. $12. 200 : 13. If £8 is gained in 12 6. If the transportation of 20 months with £100, with howcwt. 37 miles cost $16, what will much money can I gain £8 12s. in 5 months ? the transportation of 12 cwt. 50 Ans. £258. miles cost? Ans. $12.972. 14. If 200 lb. of merchandize 7. If the interest of 845 for 6 are carried 40 miles for 3 shilmonths be $1.80, what is the lings, how many pounds may be carried 60 miles for £22 14s. 6d? rate per annum ? Ans. 8 Ans. 20200 lb. per cent. 8. If 8 men spend 848 in 24 15. If for 3 shillings 200 lb. of weeks, how much will 40 men goods are carried 40 miles, how speod in 48 weeks at the same many miles may 20200 lb. be car. rate. Ans. $480. Ans. 60 miles. 16. If 200 lb. of goods are carmiles, cost 828, what will be the ried 40 miles for 3 shillings, how freight of 75 sacks of salt, each much must be paid for carrying 20200 lb. 60 miles ? weighing 21 cwt. 150 miles ? Ans. $322.159'5 Ans. 22 14s. 6d. * On this statement is founded one of the practical rules for computing inte. rest, as will be hereafter shown. 3. CONJOINED PROPORTION. CONJOINED PROPORTION is when the coins, weights, or measures of several countries are compared in the same sum. Case I. To find how many of the last kind of coin, weight, or measure, mentioned in the question, are equal to a given number of the first. RULE.*-Make the given number the third term. Of the other numbers, multiply all the antecedents together for the first term, and all the consequents together for the second ; then state the question, and proceed as in the Single Rule of Three. Examples. 1. If 10lb, at Boston make 9lb. 4. What will i lb. of pepper at Amsterdam, and 90lb. at Ain- | cost, if 3 lb. of cloves cost as terdam 1121b. at Thoulouse ; much as 6 lb. of pepper, and 2 how many pounds at Thoulouse Ib. of cinnamon cost as much as are equal to 50lb. at Boston ? 4 lb. of cloves, and 3 lb. of cinAnt. Con. namon cost 8 shillings ? 10 9 Ans. 10d. 90 112 lb. 900 : 1008 :: 50 given number. 5. If 10 lb. at London be equal 50 to 9 lb. at Amsterdam, 45 lb. at Amsterdam to 49 lb. at Bruges, 900)50400(56 Ans. and 98 lb. at Bruges to 116 lb. at 4500 Dantzick; how many pounds at Dantzick are equal to 112 lb. at 5400 London ? Ans. 1296 lb. 5100 2. If 20 braces at Leghorn much as 38 yards of ratteen, and 6. If 3 yards of cloth cost as equal 10 vares at Lisbon, and 40 vares at Lisbon 80 braces at 45 yards of ratteen are worth 5 Lucca, how many braces at Luc- gards of druggit ; how many ca' are equal to 100 braces at yards of druggit are worth 27 yards of cloth Ans. 374 yds. Leghorn ? Ans, 100 braces. 3. If 40lb. at New-York make 36 at Amsterdam, and golb. at Amsterdam make 116 at Dantzick; how many pounds at Dantzick are equal to 244 at NewYork ? Aps. 23313. * This and the following rule may often be abridged by cancelling where the same number is found among the antecedents and consequents. The proof is by several statements in the Single Rule of Three.' Case II. To find how many of the first kind of coin, weight, or measure, mentioned in the question, are equal to a given number of the last. Rule.--Proceed as in the first case, only make the product of the consequents the first term, and that of the antecedents the second. Examples. 1. If 100lb. in America make 2. If 6 braces at Leghorn make 951b. Flemish, and 191b. Flemish 3 ells English, and 5 ells Eng25lb. at Bolognia, how many i glish 9 braces at Venice, how pounds in America are equal to many braces at Leghorn will 50lb. at Bolognia ? make 45 braces at Venice ? Ans, 50 braces. Ant. Con. Ib. 1b. lb. 100 95 2375 : 1900 :: 50 3. If 20lb. at Boston make 23 25 50 at Antwerp, and 155lb. at Ant1900 475 2375)95000(40 Ans. werp make 180 at Leghorn; 190 9500 how many pounds at Boston are equal to 144 at Leghorn ? Ans. 107f1b. 19 QUESTIONS. 1. By what other name is the Dou. 7. How, if it fall under the first or ble Rule of Three sometimes second term? 8. What is Conjoined Proportion? 2. What does this rule teach? 9. How do you proceed, when it is 3. How many numbers are there u required to find how many of sually given? the last kind of coin, weight, or 4. In stating the question, how are measure, are equal to a given. the three conditional terms pla number of the first? 10. How do you proceed when it is 5. What is to be done with the other required to find how many of two terms? the first kind are equal to a 6. If the blank fall under the third given number of the last ? term, how do you proceed ? INTEREST is a premium allowed for the use of money. It is computed at so many dollars a year for the use of each hundred dollars, called so much per cent. per annum.. The principal is the sum which is upon interest. 1. SIMPLE INTEREST. Simple Interest is that which is allowed for the principal only. Case I. Rule.t 1. Multiply the principal by the rate, and divide the product by 100, the quotient will be the interest for one year. 2. Multiply the interest thus found, by the number of years, and the product will be the interest for that time. 3. If there be months and days, for the former take proportional parts of the interest for one year, and for the latter, proportional parts of the interest for one month, allowing 30 days to a month. * The rate is generally established by law. Six per cent. is the legal interest in the several New-England States, and this is to be understood in this work, where the rate is not mentioned. In New-York, legal interest is 7 per cent. + This rule is barely an application of the Single Rule of Three, or saying as 100, or £100, is to the rate, so is the principal to the interest for one year. EXAMPLE.--What is the interest of $250 for one year, at 6 per cent? As $100 : 6 :: 250 : Ans. $15. The reason for the remaining part of the rule must be obvious. When the months are not an quot part of a year, divide them into two such parts as shall be aliquot parts of a year, find the interest of those two, and add them together. The same may be done when the days are not an aliquot part of a month.“ Examples 1. What is the interest of $48.643 for 2 years, at 6 per cent per annum? Principal 48.643 To divide by 100, we have only to remove the Rate. 6 separatrix two figures from its natural place, towards the left hand. Here the answer is 1/002/91 858 found to be 5 dollars, 83 cents, 7 mills, and 16 - 1 year's int. 2.91858 hundredths of a mill. All below mills is usually rejected in practical operations. 2 yr's int. $5.83716 Ans. 2. What is the interest of $225.755 for 3 years, 8 months, and 10 days, at 6 per cent ? 225.755 6 6 mo.= =2)13.54530 interest for 1 year. 3 40.63590 interest for 3 years. .37625 interest for 10 days. $50.04235 Ans. 3. What is the interest of £86 10s. 4d. for 1 year and 6 months, at 6 per cent? £ s. d. The scholar will observe that pointing off 86 10 4 the two right hand figures for decimals, and 6 then reducing them to the next inferior de. nomination, and pointing off as before, is in £5.19 20 effect dividing by 100. 20 |