AVERAGE JUDGMENT. DEFINITION. Average Judgment, is the mean, or middle Judgment, of several persons, who are appointed to appraise any particular property. RULE. Add together the several sums which the commodity is appraised at, for a dividend; and the number of appraisers for a divisor; divide, and the quotient will be the mean, or middle Judgment required. Examples. 1. What is the value of a piece of land, which is valued by A. at $10; by B. at $11.50; by C. at $12.30; and by D. at $13:40 cts. per acre? 2. A. B. C. D. E. and F. were appointed to appraise a certain estate; they appraised it as follows, viz. A. at 83470; B. at $3650; C. at $3700; D. at $3500; E. at $3400; and F. at $3600; I demand the value of the estate. Ans. $3553.33 cts. 33 m. 3. M. N. O. and P. appraised the ship Lucy as follows, viz. M. at $6700; N. at $9000; O. at $8750; and P. at $7380; what is the middle judg-ment? Ans. $7957.5 dimes. GLE SINGLE RULE OF THREE DIRECT. DEFINITION.-The Single Rule of Three Direct teaches, by having three numbers given, to find a fourth, that shall have the same proportion to the third, as the second has to the first. If more re quire more, the proportion is direct; if less require less, the proportion is also direct; more requiring more, is when the third term is greater than the first, and the sense of the question requires that the fourth term should be greater than the second; less requiring less, is when the third term is less than the first, and the sense of the question requires that the fourth term should be less than the second. RULE.-State the question, or arrange the three given numbers in such order, that the one which asks the question may stand in the third place ;* that number which is of the same name with the third, must possess the first place; the remaining number (which is always of the same name with the number required) must possess the middle place. Reduce the first and third terms, or numbers, into the same denomination; and reduce the middle number, or term, into the lowest denomination mentioned; then multiply the second and third terms together, and divide the product by the first; the quotient will be the answer, or fourth term sought; and always will be of the same denomination as the middle term was in when it was multiplied with the third term; and may be reduced to any other denomination required." Rule of Three in Decimals, Rule.-State the question as in the Rule of Three Direct; prepare the terms by reducing the smaller denominations to the decimal of the highest; observing that the Integer in the first and third terms are in the same denomination; multiply and divide as in thee Rule of Three Direct, and point off for decimals as is required in the rule of multiplication and division of decimals. * The third term always asks a question and is generally preceded by some such words as, what will? How much? How far? How long? How soon? What is? Where will, &c. ? F 62 SINGLE RULE OF THREE DIRECT, &c. NOTE. As the currency of the United States is a decimal calculation, the decimal mode of computing becomes much the easiest, and for the benefit of the learner, I have done the questions in the Rule of Three by both methods, therefore one serves as a proof to the other. Examples. 1. If ten sheep are worth $22.22; what are 19 of the kind worth? Sheep D. cts. sheep. As 10: 22.22 :: 19 19 19998 2222 10)422.18 42.218 $42.21 cts. 8 m. Ans. NOTE. In the first question 19 sheep is the number that asks the question, and is placed in the third place; 10 being of the same name, viz. sheep, it is placed in the first place, and the remaining number, viz. $22.22 cents, is the number left and is used for the middle term; and is of the same name with the number sought, viz. money. The same question done by direct proportion. NOTE. In this example the first and third terms are of the same name, they need no reducing; there being cents mentioned in the middle term, I reduced the whole to cents, and the answer came in cents; which I divided by 100 to bring them into dollars. 2. If 20 acres, I rood, 20 rods of land, cost $183.37 cts. 5 m.; what will 37 acres of the same kind be worth? 20 acres, 1 rood, 20 rods 20.375 acres. Acres dolls. acres. As 20-375: 183-375 :: 37 $333 Ans.. NOTE-In this example I reduced the 1 rood, 20 rods. to the decimal of an acre; then I multiplied and divided according to the rule of decimals. The same question done by direct proportion. Acr. rood rds. D. cls. m. acres. Ans. $333. As 20 1 20: 183.37.5 :: 37 NOTE. In this example there being rods in the first term, I brought all the first term into rods, and also brought the third term into rods; and the middle term into mills; then multiplied and divided according to rule, the answer came in mills. 3. If 23 cwt. 3 qrs. of sugar is worth $261.25 cts; I demand what must be given for 2 cwt. 1 qr. of the kind. Ans. 24 dols. 75 cts. The same question done by direct proportion. Ans. $24.75 4. What will 4 hhd. of rum come to, containing as follows, viz. the first 101, the second 96, the third 894, and the fourth 1113, gallons; if 6 gallons cost $6.89? Ans. $423.20 cts. 5 m. The same question done by direct proportion. Ans. $423.20 cts. 5 m. 5. If 1000 feet of boards are worth $11.12 cents; I demand the price of 17221 feet. Ans. $191.49 cts. 7 m. The same question done by direct proportion. Ans. 191.49.7† m. 6. If of 6 be three; I demand the value of of 20 Ans, 7.5 64 SINGLE RULE OF THREE DIRECT, &c. The same question done by direct proportion. Ans. 7 7. If 62 dozen pigeons are worth 65 cents; I demand the price of 29 dozen. Ans $2.97 cts. 5 m. The same question done by direct proportion. 1 Ans. $2.97.5. 8. If 65 bushels and 1 peck of corn were spent in a family of 6 persons; I demand the quantity that would be sufficient to support a family of 22 persons for the same time. Ans. 239.25 bushels. The same question done by direct proportion. Ans. 2391 bushels. 9. How long will 34261 lbs. of beef last an army. of 600 men ; allowing them to draw 4 ounces each, and that 3 times per day?" Days 675476 Ans. 67100 The same question done by direct proportion. Ans. 67478 days. 100 10. How many times would a wheel, that is 16 ft. 3 inches in circumference, turn round in going round the world on the Equator; allowing a degree there to contain 691 miles ? Ans. 8129575182 The same question done by direct proportion. Ans. 8129575-79. 11. How far are the inhabitants of the equator carried in a minute; allowing the earth to make one revolution in 24 hours contain 69. miles? The same question done and allowing a degree to by Ans. 17 mi. 3 fur. direct proportion. 12. A merchant failing in trade, is owing $6420 20 cents; his effects are worth $3142.75 cents; what will A. lose to whom he owed $960.73 cents? Ans. $490.44. The same question done by direct proportion. Ans. $490.44†. |