KEY TO CARD No. 31. OPERATION. b. s. b. 144: 50:: 12 50 600s. Pence in a shilling, 12 First term, 144)7200(50d. 720 0 Let us query what propor tion this lesson is in. Is the third term greater than the first? we see it is; does the nature of the question show, that 120 gallons, the third term, will cost more than 32 gallons? If so, the proportion is direct. 3080, 2d. term. In this last question, the 1st. term, 32)369600(11550d. third term is less than the first, and the nature of the question requires the fourth term or answer to be less than the second: Therefore less requires less. LESSON 8. If a barrel of wine containing 32 gallons cost £12 16 8 what will a pipe of 120 gallons cost? Answer, £48 2 6. Reduce the given sum into pence. £12 16 8 20 256 12 3080 pence. g. d. g. 32: 3080:: 120 Cards are omitted till Compound Proportion. LESSON 9. If 32 gallons of wine cost £ 12 16 8 how much is that a gallon? Answer, £0 8s. Od. 1gr. As 32 gal.: £ 12 16 8 1 gal. to a fourth number. That is to say, as 32 gallons are to £ 12 16 8, so is 1 gallon to a fourth number NOTE.-As the third term is one, so multiplication is needless, and division only is necessary; therefore divide the second term £ 12 16 8 by 32 the first term. Divide as in compound division, by 4 and by 8, or by 8 and by 4. Proof of Lesson 8 and 9, by Compound Multiplication. Multiply £0 8 0 I by 120 gallons. Multiply by 10 and by 12. £0 8 0 1 10 4 022 12 £48 2 6 0 LESSON 10. If a servant procure 374 cents a week, how much will he When a man earns 125 dollars a year, that is, in 365 days, how much may he spend each day and lay up 53 dollars 82 cents at the year's end? Ans. 19 cents each day. DIRECTIONS. In the first place annex two ciphers to 125 to reduce the dollars to cents, thus, Subtract 53 dol. 82 cents or Cents remain, 12500 cents. 5382.5 7117.5 This sum 5382.5 cents is, as if it were taken out from the whole sum, and deposited in the chest. Then there remain 7117.5 cents for spending money to be divided into 365 parts. We must now study inverse proportion. When the third term is greater than the first, and the nature of the question requires the fourth term to be less than the second, then the proportion is inverse. This is called more requires less. EXAMPLE. If 4 men can harvest a field of wheat in 2 days, in what time can 8 men do the same work? Answer, 1 day. RULE. Multiply the first and second terms together and divide the product by the third, the quotient will be the fourth In this example the fourth term is as much less than the second, as the third is greater than the first: For, 8 is twice the quantity of 4, but 1 is only half the quantity of 2. Therefore this sort of proportion is properly named inverse ; or, indirect, or, if you please, contrary. AGAIN. When the third term is less than the first and requires the fourth to be greater than the second, the proportion is also inverse. This is called less requires more. EXAMPLE. If 12 persons in a family have provisions for 36 days, how many persons will the same provisions serve 18 days? Answer, 24 persons. 36: 12: 18 to a fourth number, 24. That is to say, if 36 days require 12 persons to devour the food, what number of persons will 18 days require? Here the third term is less than the first and requires the fourth to be contrary, that is, as much greater than the second. For, the third term is only half the quantity of the first, but the fourth term is double the quantity of the second. OPERATION. 36 first term. 12 second term. 18)432(21 persons, Answer. 36 .72 72 LESSON 12. If 864 feet in length of plank 12 inches wide will floor a room, how much in length will be required when the planks are 18 inches wide? Answer, 576 feet in length. If 500 dollars draw 35 dollars of interest in 12 months, what sum will give the same interest in 3 months? mo. dol. mo. 12: 500 :: 3 3)6000(2000 OPERATION. Answer, 2000 dollars. If 12 months require 500 dols. 3 months will require four times that sum, LESSON 14. If 24 horses will eat 36 bushels of oats in 14 day, what number of horses will eat the same quantity in 3 days? If 56 pounds of butter cost £0 18 8 what is that a |