9. There are 780 pupils in school, and 40% are males. How many are males ? 10. If a man buys a horse for $150 and sells it at a profit of 20 %, how much does he gain ? In each of the preceding problems we have two terms, a per cent and a whole or a mixed number. The per cent in each problem the multiplier, and is called the rate. The whole or the mixed number is the multiplicand, and is called the base. The product is called the percentage. The base is that number of which some per cent is to be taken; as, 5% of $200 (base). The rate is the number of hundredths taken; as, 5% (rate) of 80 horses; that is, 16 of 80 horses. The percentage of a number is the result obtained by taking any per cent of it; as 10% of 200 acres is 10 of 200 acres, or 20 acres (percentage). 11. What is 75% of $5.12 ? MULTIPLIER MULTIPLICAND PRODUCT Base Percentage 75% of $5.12 ( ) Decimal Method Study of Problem 75% = .75. What is the base ? $ 5.12. What is the $5.12 = base rate? 75% To what do the base and rate correspond .75= rate in simple multiplication ? Multiplicand 2560 and multiplier. 3584 To what does percentage correspond in $3.8400= percentage simple multiplication? Product. How is the product found in simple Fractional Method multiplication ? Multiplier x multiplicand. 75% = $ How is the percentage found ? Rate base. of $5.12= $3.84 The percentage of a number equals the product of the base by the rate. Find: 17. 8 % of 400. 20. 6% of 150 lb. 16. 5% of 100 acres. 21. 11 % of $75. 22. 80 is the base, 25% is the rate, find the percentage. 23. A house costs $2500, and the damage by fire is 8%. Find the amount of the damage. 24. John owes his tailor $ 80, and pays 371 %. How much does he still owe him ? 25. Mary spells 90 % of 80 words correctly. How many does she miss ? 26. A boy buys apples at $1 per bushel, and sells them at a profit of 20%. How much profit is that per bushel ? 27. 61 % of 3680 equals what number? 28. A man buys a farm for $2500, and sells it for 25 % more than it cost him. For how much does he sell the farm? 29. A man earns $180 per month, and puts 331 % of it in the savings bank. What is his deposit each month ? 30. If 371 % of a man's farm is in timber, and the total area is 240 acres, how much timber land has he ? 31. A teacher who earned $1200 a year spent 663 % of her salary. How much did she save? 32. Mr. Scott's horse is valued at $ 250 and Mr. Hill's at 60% of this. What is the value of Mr. Hill's horse ? 33. The population of a town of 9672 inhabitants increased 121 % in a year. What was the increase in population ? Finding what per cent one number is of another number. 1. What % of 8 is 4 ? 4 is of 8, or 50% of 8. What % of: 2. 10 is 5 ? 7. 12 is 9 ? 12. 121 is 64 ? 3. 12 is 6 ? 8. 20 is 15 ? 13. 271 is 51 ? 4. 20 is 5 ? 9. 25 is 5 ? 14. 22, is 71? 5. 12 is 4 ? 10. 40 is 8? 15. 171 is 31 ? 6. 16 is 8? 11. 30 is 10 ? 16. 194 is 6}? Written Work 1. What per cent of 40 is 10? Since the percentage equals the 10+ 40 = 18 = .25 or 25% base multiplied by the rate, the rate Test: .25 x 40 = 10. must equal the percentage divided by the base. 10 = 40 = 8=.25 or 25%. The rate equals the percentage divided by the base. 11. Frank's salary for a month is $75 and Samuel's is $ 25. What per cent of Frank's salary is Samuel's ? 12. I earn $600 a year and spend $300. What per cent of my money do I spend ? 13. A farmer who raised 350 bushels of potatoes marketed only 280 bushels. What per cent of his potatoes did he market? Finding a number when a per cent of it is given. 5 is or 1 of 10. Find the number of which : 3. 10 is 25% 8. 40 is 20% 9. 10 is 5% 10. 50 is 121 % 11. 30 is 66 % 12. 50 is 621 % Written Work 1. Find the number if 25% of it is 128. 128 : .25=512 Since the percentage equals the base multiplied by the rate, the base equals the Test: .25 x 512= 128 percentage divided by the rate. 128 = 25 512, the number. The base equals the percentage divided by the rate. Find the number if : 2. 10% of it is $35 8. 621 % of it is $75 3. 20% of it is $38 9. 75% of it is $96 4. 30% of it is $45 10. 60% of it is $84 5. 121 % of it is $56 11. 8% of it is $24 6. 331% of it is $65 12. 35% of it is $42 7. 371 % of it is $72 13. 871 % of it is $70 14. A boy paid $3 or 20% of his month's pay for a pair of shoes. How much does he earn in a month ? 15. A teacher pays $20 per month for board, and this is 40% of his salary. What is his monthly salary? GAIN AND LOSS When people buy or sell, they always reckon their profit or their loss on what a thing costs. 1. A boy buys bananas at 30 cents per dozen and sells them at 331% gain. For how much does he sell the bananas per dozen ? The gain is of 304, or 109 per dozen. Therefore the selling price is 309 + 10%, or 40 $ per dozen. 2. Bread is bought at 5 cents a loaf and sold at 6 cents. What is the gain per cent ? The gain on 1 loaf is 14. 19 = 1 of 5% = 20% gain. 7. If a dealer buys shoes at $18 a dozen pairs and sells them at 50 % gain, what is the retail price? 8. A boy buys oranges at 40¢ a dozen and sells them at 5$ apiece. What per cent does he gain? 9. A man buys a horse for $150 and sells it for $175. What per cent does he gain? 10. A boy buys a pony for $50 and sells it for $62.50. What per cent does he gain? 11. A man sells a city lot that cost him $1200 at a loss of 15%. Find the amount he loses. 12. A merchant buys goods at $.75 per yard and retails them at a profit of 40 %. Find the gain on 36 yards. HAM. INT. ARITH. — 16 |