PERCENTAGE. 379. ILL. Ex. What is 3o of $300. Ans. $21. A number, as $21 in the ILL. Ex., found by taking a number of hundredths of a given number, is Percentage. Define percentage. NOTE. The word "percentage" is derived from the Latin "per centum," which means by the hundred. 380. The number of which a number of hundredths are taken for a percentage, as $300 in the ILL. Ex., is the basis of percentage. Define basis of percentage. 381. The number of hundredths of the basis which are taken to obtain a percentage, as 7 in the ILL. Ex., is the rate per cent. Define rate per cent. NOTE. The sign % is used for the words "per cent." 382. 2 per cent may be expressed .02 or 1 or 2%. Thus any rate per cent may be expressed either decimally, in the form of a common fraction, or by the sign %. number? OPERATION. Ans. 1. 26. 37%. Ans. 1800. Ans. 100. What per cent of a number is of the Explanation. Since any number equals 100% of itself, of the number equals † of 100% or 20%. 31. 16%. = 32. 81%. 5) 100% 20% EXAMPLES. 33. What % of a number is 34. What % of a number is 35. What % of a number is Ans. 20%. ? ? ? of the number? of the number? ? ? ? of the number?? § ? &? 384. TO FIND THE PERCENTAGE WHEN THE BASIS AND THE RATE PER CENT ARE GIVEN. ILL. Ex. What is 5% of $20 ? From the above we derive the following RULE. To find the percentage when the basis and rate per cent are given: Multiply the basis by the rate per cent and divide by 100. EXAMPLES. 36. What is 6% of $75? Ans. $4.50. 37. What is 10% of $180? 73% of 200 days? 38. What is the difference between 8% of $ 450 and 61% of $680 ? Ans. $61. 385. TO FIND THE AMOUNT OR REMAINDER, WHEN THE BASIS AND THE RATE PER CENT ARE GIVEN. ILL. Ex. At a certain time A and B each owed $ 300; in one year A's debt was increased 20% and B's was diminished 20%, what was then the amount of A's debt? What remained of B's? Explanation.-20% of $ 300 is $ 60, which is the percentage of increase of A's debt, and of decrease of B's; $ 300+ $60 $360, amount of A's debt. $ 300. $60 = = $240, what remained of B's. The basis plus the percentage is called the amount. The basis minus the percentage is called the remainder. The amount may be found by taking 120 of the basis, and the remainder by taking of the basis. RULE. - 80 Hence the following To find the amount or the remainder when the basis and rate per cent are given: Multiply the basis by 100 plus or minus the rate per cent, and divide by 100. EXAMPLES. 39. A merchant had 7000 tons of coal, and shipped 65% of it; how much had he left? Ans. 2,450 tons. 40. At what price must a chair be sold which cost $1.25 that 10% may be gained? Ans. $1.37. 41. A mechanic sold a shop which cost him $800 at a loss of 121%; what did he receive for it? 42. A man willed to his sons John and William $5500 each; within one year John spent 73% of his money and William increased his 12%; at the end of the year how much more money had William than John ? 43. A trader sold 100 pairs of gloves at $.80 per pair; 5% of the price was deducted for prompt payment; what was the sum deducted? what was the balance paid? Ans. $4 deducted; $ 76 paid. NOTE. That part of the nominal price of goods which is deducted, as $4, in the above example, is called a discount. 44. A lot of crockery was sold for $128; if a discount of 6% was made for prompt payment, what was the balance paid? Ans. $120.32. 45. What is the balance of a bill of $270 for books after a discount of 333% has been made? 46. What is the balance of a bill of $ 64.50 after two discounts have been made; the first of 20% on the $64.50, the other of 5% upon what then remained? Ans. $ 49.02. 386. TO FIND THE BASIS WHEN THE RATE PER CENT AND THE PERCENTAGE ARE GIVEN. ILL. Ex. A man lost $ 63, which was 9% of all the money he had; how much money had he? From the above we derive the following RULE. To find the basis when the rate per cent and the percentage are given: Divide the percentage by the rate per cent and multiply by 100. EXAMPLES. 47. A man rents a house at $ 575 a year, which is 10% of its valuation; what is its valuation? Ans. $5,750. 48. A lawyer charged $7.50 for collecting money, which was 6% of what he collected; how much did he collect? 49. A man failing in business pays 25% of what he owes ; if he pays one creditor $ 250.75, what did he owe him? 50. If the percentage is $ 18.75 and the rate 5%, what is the basis? Ans. $375. 51. If the percentage is 37 bushels and the rate 8%, what is the basis? Ans. 4682 bushels. For Dictation Exercises upon these examples, see Key. 387. TO FIND THE BASIS, WHEN THE AMOUNT, OR THe Re MAINDER, AND THE RATE PER CENT ARE GIVEN. ILL. Ex. I. After adding 5% to the weight of a lot of hay by salting, the weight was 1869 lbs. ; what was the weight before salting? OPERATION. 89 20 1869 X 100 105 = 1780 21 Explanation. If 5% was added to the weight, the amount, 1869 lbs., must be 105% of the weight. If 1869 lbs. is 105 of the weight, must be of 1869 lbs., and 188 must be (1 of 1869 lbs.) X 100 = 1780 lbs. Ans. 1,780 lbs. ILL. EX. II. How many soldiers were there in a regiment at first, which, after losing 8% by sickness, has 644 remaining? Explanation. Since 8% are lost, 92% remain. If 644 soldiers are 9 of the regiment, must be of 644 soldiers, and must be (of 644 soldiers) X 700 soldiers. Ans. 700 soldiers. 100 = From the above we derive the following rules. RULE I. To find the basis, amount and rate per cent being given: Divide the amount by 100 plus the rate per cent, and multiply by 100. RULE II. To find the basis, remainder and rate per cent being given; Divide the remainder by 100 minus the rate per cent, and multiply by 100. EXAMPLES. 52. What should be the weight of a loaf of bread before baking, that it may weigh 30 ounces afterwards, if in the process of baking it loses 61%? Ans. 32 oz. 53. A certain school has now 84 pupils, which is 50% more than it had last year; how many had it last year? 54. After increasing the wages of his workmen 38%, a manufacturer paid his operatives $2 a day; what did he pay them before? Ans. $1.50. |