266. Illustrative problems. 1. I have thought of a number; I add 7 to it; then I subtract 3; the result is now 28. What is the number? 1. Let x the number. Then x + 7 is the number with 7 added, and x + 4 is the remainder after subtracting 3, and the problem tells us that this remainder equals 28. 2. Therefore x + 4 = 28. 3. Subtracting 4 from both sides, x = 24. To check this, put 24 in the statement of the problem. 2. What number is that which, being doubled, and 7 being then added, equals 29? 1. Let x = the number. Then 2 x = double the number, and 2 x + 7 = double the number with 7 added, and the problem tells us that this equals 29. 2. Therefore 2 x + 7 = 29. 3. Subtracting 7 from both sides, 2 x = 22. 4. Dividing both sides by 2, x = 11. WRITTEN EXERCISE 1. What number multiplied by 1 equals 96? 2. What number multiplied by 1.04 equals 7.28? 3. If 5 times a certain number, less 70, is 80, what is the number? (Solve also without using x.) 4. If 72 times a number, together with 72, is 792, what is the number? (Solve also without using x.) 5. If to twice a number I add 15, the result is 75. What is the number? (Solve also without using x.) 6. I have thought of a number; I add 7; I add this result to itself; I take away 12; the result is 42. Required 267. Illustrative problems. 1. A horse and carriage together cost $375, and the carriage cost twice what the 2. Therefore 3x = 375, because x (that is, 1 x) and 2 x are 3 x. 3. 66 x = 125, by dividing both sides by 3. Therefore the horse cost $125. 2. After increasing 6%, a certain sum amounts to $318. What is the sum? Therefore the sum is $300, as is easily proved. WRITTEN EXERCISE 1. After gaining 12%, a certain sum amounts to $392. What is the sum? 2. If to of a certain number I add 730, the result is 855. What is the number? 3. A boy lost of his marbles and had 18 left. How many had he at first? 4. A man sold of his cattle and had 68 left. How many had he at first? 5. A certain sum was increased 50% and then amounted to $505.50. What was the sum? 6. If your father is 3 times as old as you, and if the sum 268. Illustrative problem. A man sold a carriage for $120, which was 20% less than it cost. How much did it cost? Therefore the cost was $150, as is easily proved. WRITTEN EXERCISE 1. A man sold a house for $2250, which was 20% less than it cost. How much did it cost? 2. With the $2250 he bought 20 acres of land from Mr. A, who thereby gained 25% on what it cost him. How much did Mr. A pay per acre for the land? 3. A man sold a farm of 100 acres at the rate of $56.25 an acre. He lost 10% on the cost of the farm. How much did the farm cost him? 4. A dealer bought two horses at the same price. He sold one, at a profit of 20%, for $102. The other he sold at a loss of 10%. How much did he receive for the latter? 5. A certain village, after gaining 10% on its population in 1900, had 10% less population than another village of 4180 inhabitants. What was the population of the first village in 1900? 6. A furniture dealer bought 5 sets of furniture at $65 a set, 3 at $90, and 2 at $40. The $40 sets he sold at a profit of 30%, the $65 sets at a profit of 20%, but on the PERCENTAGE ORAL EXERCISE 1. Express as per cents: 1,, b, b, b, f. 3. Express as per cents:, 3, 3, t, fo, fo, fo. 4. If g of a number is 9, what is the number? 5. If 371% of a number is 6, what is the number? 6. If 62% of a number is 15, what is the number? 7. If 75% of a number is 66, what is the number? 8. Express as common fractions: 20%, 331%, 871%. 9. Express as common fractions: 61%, 81%, 121%. 10. How much is 25% of $8000? 33% of $9000 ? 11. How much is 163% of $120? 10% of $225.50 ? 12. If 87% of a number is 1400, what is the number? 13. 30 is 163% of what number? 33% of what number? 14. 40 is 66% of what number? 833% of what number? 15. Tell the short way of finding 121% of a number; of finding 66% of a number. 16. Tell the short way of finding 61% of a number; of finding 163% of a number. WRITTEN EXERCISE 1. 371% of $164. 9. 150% of $2178. 2. 61% of $33.60. 266. Illustrative problems. 1. I have thought of a number; I add 7 to it; then I subtract 3; the result is now 28. What is the number? 1. Let x = the number. Then x+7 is the number with 7 added, and x + 4 is the remainder after subtracting 3, and the problem tells us that this remainder equals 28. 2. Therefore x + 4 = 28. 3. Subtracting 4 from both sides, x = 24. To check this, put 24 in the statement of the problem. 2. What number is that which, being doubled, and 7 being then added, equals 29? 1. Let x the number. Then 2 x = double the number, and 2 x + 7: = double the num ber with 7 added, and the problem tells us that this equals 29. 2. Therefore 2 x + 7 = 29. 3. Subtracting 7 from both sides, 2 x = 22. 4. Dividing both sides by 2, x = 11. WRITTEN EXERCISE 1. What number multiplied by 1 equals 96? 2. What number multiplied by 1.04 equals 7.28? 3. If 5 times a certain number, less 70, is 80, what is the number? (Solve also without using x.) 4. If 72 times a number, together with 72, is 792, what is the number? (Solve also without using x.) 5. If to twice a number I add 15, the result is 75. What is the number? (Solve also without using x.) 6. I have thought of a number; I add 7; I add this result to itself; I take away 12; the result is 42. Required |