CHAPTER VI. SECTION I. PERCENTAGE 288. Per cent (contraction for per centum) means, by the hundred. Thus, 5 per cent of $1 is 15 of a dollar, or 5 cents. The term percentage, as commonly used, has two meanings. 289. 1. It is the name of a process of computing by hundredths. Thus, finding the value of 5 per cent of a dollar, is working an example in percentage. 290. 2. It is a name applied to any number of hundredths of anything that is regarded as a basis of computation. Thus, in the example 5 per cent of $1 = 5c., 5c. is the percentage, $1 the basis, or base. Per cent is frequently used in the same sense as the second meaning of Percentage. 291. Rate per Cent is the number of hundredths. Thus, in the expression 6 per cent of $1, 6 is the rate per cent. In computations, we give the rate per cent a denominator 100, and thus obtain a common or decimal fraction called 292. The Rate, an expression denoting what part of 291 the base equals the percentage. Thus, in 6 per cent of $1 = 6c., the rate is 180, 3%, or .06. 293. The Base of percentage is that number of which a certain per cent is computed. 294. The Amount is the sum of the base and percentage. 295. The Difference, or Remainder, is the Base less the Percentage. 296. Rate per cent is usually written with the sign %. Thus 5 per cent may be written 5%. The sign %, is always read "per cent." Thus, 6% is read "Six per cent." NOTE. The sign is generally used in business, but in calculations rate only is used, and is written as a decimal or common fraction. 4 61 100' Thus, the rate per cent 61 is the rate or, or .061, or .0625; the 12 rate % 12 is the rate or, or .121, or .125. One per cent of a number is of that number; less than one per cent of a number is less than of that number. One hundred per cent of a number is that number, because it is 188 of the number. Two hundred per cent of a number is twice that number, or 188 of it; etc. Table showing what part of anything a certain rate % of 66 66 121 66 66 297. Base and Rate per cent given, to find Percentage. Oral Exercises EXAMPLE 1.-5% of $10 is what part of it? 10%? SOLUTION.-5% of $10 is 150, or of it. 10% of $10 is 10% to of it. or EXAMPLE 2.-How much is 5% of $10? 10%? SOLUTION.-5% of $10 is 15, or of $10 = 50%. 10% of $10 is 13. A merchant gained in one year 28% of his capital. What part of his capital equals his gain? 14. A man whose farm contained 280 acres, bought as many acres more as equaled 10% of what he already had. How many acres did he buy? 15. In a school of 300 pupils, 40% are girls and the remainder are boys. How many of each? 16. A gentleman bequeathed 20% of his estate to a college, 10% to an orphan asylum, and 10% to a public library, and the remainder he gave to his children. What % of his estate did the children receive? 17. Suppose there were three, how many % would that be for each; and what part of the estate would each receive? 18. Suppose the estate worth $200000; how much would each child receive? Written Exercises EXAMPLE.-Find 15% of 30 bu. of wheat. 1ST SOLUTION. 30 bu. Base. .15 Rate. 4.5 bu. Percentage. EXPLANATION.-15% of 30 bu. is the same as .15 of 30 bu. and .15 of 30 bu. is 4.5 bu. Therefore, 15% of 30 bu. is 4.5 bu. EXPLANATION.-Since 15% means 15 hundredths, we take that part of 30 bu. that 15% is of 100%, that is, 100, or of 30 bu. = 4 bu. Ans. NOTE. We might solve the Example by Proportion, thus: 100% 15%. : 30 bu.: (43) bu. 298. RULES.-I. Multiply the Base by the Rate. II. Take that part of the Base that the given rate % is of 100% PROBLEMS. 1. Find 25% of 64 horses. 2. Find 35% of $125. 3. Find 45% of £13†5. 7. Find 1% of $2.25. 8. Find 3% of 7.5s. 10. Find 121% of a ship. 11. Find 163% of an oil-well. 12. Find 331% of an iron-mill. 13. Find 133% of $100. Ans. 16 horses. Ans. $43.75. Ans. £5.88. Ans. 1.65 A. Ans. 3.885 bu. Ans. .474375 mi. Ans. of a ship. Ans. of an oil-well. Ans. of an iron-mill. 14. The distance from Pittsburgh to Philadelphia is 355.2 mi., and from Pittsburgh to New York is 25% more. is the distance from Pittsburgh to New York? What Ans. 444 mi. 15. The distance from New York to Pittsburgh is 444 mi., and the distance from Philadelphia to Pittsburgh is 20% less. What is the distance between the two latter places? Ans. 355.2 mi. |