MISCELLANEOUS EXAMPLES. 126. A owned and of a ship, which he sold for $ 3650, and B owns xo of her, which he wishes to sell at the same rate. What must be B's price? Since the price of a of the ship is $ 3650, the price of the whole ship must be 4 of $ 3650, which is $ 17520; and 1. of $17520 is $ 5256, which must be B's price. 127. If 3650 be of some number, what is id of the same number? 128. A merchant has bought of a company's stock, for $92000. What would be the price of 2 of the stock, at the same rate ? 129. A merchant owning in of a ship, sold 2 of what he owned for $1841. What is the value of the whole ship, according to this sale ? 130. 1841 is of 12 of what number? 131. After a certain tract of land had been equally divided arnong 16 owners, one of them sold į of his share at $5, an acre, and received $444. How much land was there in the whole tract ? 132. If 16 of a yard of cloth be worth of a dollar, what is the value of į of a yard? Since 16 of a yard is worth of a dollar, a yard is worth 14 of ã of a dollar, which is a 2 of a dollar; and 11 of a yard is worth ii of of a dollar, which is 22.9 of a dollar, or $ 1462=$11=$ 1.559 +: 133. If of a yard of lace be worth is of a dollar, what is to of a yard worth? 134. If of a barrel of flour cost 4 dollars, what is the cost of 6 barrels, at the same rate ? 135. If 13? bushels of corn cost 7 dollars, what is the price of 9 bushels, at the same rate ? 136. If 42 pounds of indigo be worth $87.625, what is the value of 192 pounds ? 137. A garrison of 900 men have provision for. 4 months. How many men must leave the garrison, that the provision may last the remainder 9 months ? 138. If a loaf of bread weighing 32 ounces be sold for eight cents, when flour is worth $6.50 per barrel, what 1 ought the eight-cent loaf to weigh, when four is worth only $5 a barrel ? 139. A company of 75 soldiers are to be clothed; each suit is to contain 34 yards of cloth, 6 quarters wide, and to be lined with flannels of a yard wide. How many yards of flannel will be required? 140. If a garrison of 1500 men consume 750 barrels of flour in 9 months, how many barrels will 2150 men consume in 15 months ? 141. How many tiles 8 inches square, will hearth 16 feet long, and 12 feet wide? 142. If the expense of carrying 17 cwt. 3qr. 14 lb. 85 miles be $23.84, what will be the expense of carrying 53cwt. 2qr. 150 miles, at the same rate ? 143. Two men bought a barrel of flour; one paid 3 dollars, and the other paid 3 dollars. What part of the flour should each of them have ? 144. If the corn contained in 8 bags, holding 2 bushels 3 pecks each, be worth $ 14.25, what is the value of the corn contained in 7 bags, each holding 2 bu. 3 pk. 7qt.? 145. A ship of war sailed with 650 men, and provision for a cruise of 15 months. At the end of 3 months she captured an enemy's vessel, and put 75 men on board of her. Five months after, she captured and sunk another vessel, and took on board the crew, consisting of 350 How long did the provision last, from the comnencement of the cruise ? 146. A built 156 rods of wall in a certain time, and B m the same time built 13 rods to every 12 that A built. They were paid $ 1.25 per rod. How much did B receive more than A ? 147. A father bequeathed $ 6000 as follows; viz. s to his wife, } to his son, i to his daughter, and the remainder to his servant. How much did each receive ? 149. If 1} of a pound of sugar be worth of a shilling, what is the value of of a cwt.? 149. If 75.15 gallons of water, in one hour, run into a cistern, which will hold 6 hogsheads, and by a pipe 241 gallons an hour run out, in how many hours, minutes and seconds will the cistern be filled ? men. XIV. PERCENTAGE. Under this head may be classed, those computations which investigate the value of a given number of hundredths of any quantity. The number of hundredths to be taken or considered in any number, is called the per cent. The term, per cent., is an abbreviation of per centum, which signifies by the hundred. Any per cent. is conveniently expressed by a decimal. Thus, i per cent. of any number is .01 of that number; 8 per cent. is .08; 25 per cent. is :25; &c. 1. A merchant, who has 1426 dollars deposited in the bank, wishes to draw out 5 per cent. of his deposite. How many dollars must he draw ? Since 5 per cent. of any quantity is 1426 that quantity, the question to be solved in this .05 example is- What is 1.7 of 1426 dollars? Or, $71.30 decimally— What is .05 of 1426 dollars ? The answer is conveniently found by multiplying 1426 by .05. The whole number in the product expresses dollars, and the decimal expresses cents. 2. A trader, who went to the city with 321 dollars, to purchase goods, laid out 9 per cent. of his money for coffee. How many dollars did he pay for coffee 3. What is 1 per cent. of 100 dollars ? 4. What is 1 per cent. of 834 dollars ? 5. What is 3 per cent. of 100 dollars ? 6. What is 3 per cent. of 42 dollars ? 7. What is 6 per cent. of 100 dollars ? 8. What is 6 per cent. of 99 dollars ? 9. What is 7 per cent. of 100 dollars ? 10. What is 7 per cent. of 1000 dollars ? 11. What is 8 per cent. of 26 dollars ? 12. What is 9 per cent. of 354 dollars ? 13. What is 10 per cent. of 2244 dollars ? 14. What is 16 per cent. of 13 dollars ? 15. What is 37 per cent. of 211 dollars ? 16. What is 99 per cent. of 100 dollars ? 17. What is 100 per cent. of 48 dollars ? 18. A trader laid out 1214 dollars as follows. He paid 24 per cent. of the money for broadcloths; 38 per cent. for linens; 8 per cent. for calicoes; and the remainder for cottons. How many dollars did he pay for each kind of goods ? When the rate per cent. is a vulgar fraction, or a mixed number, the fraction may be changed to a decimal. Observe, that, 1 per cerrt. when expressed decimally, is .01; therefore a fraction of 1 per cent. when reduced to a decimal, becomes so many tenths, hundredths, &c. of a hundredth. For example, as of 1 unit is .25 of a unit, so of 1-hundredth is .25 of a hundredth, and is denoted thus, .0025. 19. What is 31 per cent. of 243 dollars ? 3 per cent. =.03 243 1215 8.505 Ans. $8.507 per cent, of 61 dollars ? 25. What is per cent. of 9487 dollars ? 26. If 8} per cent. be taken from 36 dollars, how many dollars will there be remaining ? 27. A merchant who had 400 barrels of flour, shipped 42} per cent. of it, and sold the remainder. How many barrels did he sell ? 28. A trader bought 800 pounds of coffee; and, in getting it to his store, 2 per cent. of it was wasted. How many pounds did he lose? What did the remainder amount 10, at 13 cents a pound ? 29. Two men had 120 dollars each. One of them paid out 14 per cent. of his money, and the other 17 How many dollars did one pay more than the other? per cent. 7} 114 30. Find 7} per cent. of $ 344. When there is a fraction in the 344 • 100=3.44 rate per cent. which cannot be exactly expressed by a decimal 2408 as in this example — we first fina' 1 per cent. of the given sum, by dividing it by 100; that is, by cut $25.22 ting off two decimal figures, and then multiply this quotient by the mixed number expressing the rate per cent. 31. What is 45 per cent. of 624 dollars ? 32. What is 6 per cent. of 38 dollars ? 33. What is 3 per cent. of 2310 dollars ? 34. What is 9 per cent. of 17 dollars ? 35. What is 81 per cent. of 152 dollars.? 36. Find the difference between 5 per cent. of 41 dollars, and 4 } per cent. of 39 dollars. 37. What is 7 per cent. of $ 24.32 ? Here we have cents (decimals] in the num 24.32 ber on which the percentage is to be taken. .07 We however multiply as usual in decimal multiplication; and the first two decimal fig $ 1.7024 ures in the product express cents, the third figure expresses mills, and the fourth expresses tenths of a mill. 38. What is 14 per cent. of $641.94 ? 39. What is 4 } per cent. of $37.26 ? 40. What is 11} per cent. of $ 150.75 ? 41. What is 12 per cent. of $ 25.32 ? 42. If a horse and gig cost 400 dollars, and the gig cost 32 per cent. of the sum, what did the horse cost? 43. Find the difference between 13 per cent. of $18.09, and 7 per cent. of $41. 44. Find the difference between 9 per cent. of $ 16, and 8 per cent. of $ 17.30. |