cost? 5. If 8 acres produce 176 bush 14. A owes B £296 17s. but els of wheat, what will 34 acres becoming a bankrupt, can pay produce? only 7s 6d on the pound ; how Ans. 748 bushels. much will B receive ? 6. If 9]b. of sugar cost 6s. what Ans. €111 68 4d 2qrs. will 25lb cost? Ans. 16s. 8d. 15. If one dozen of eggs cost When there is a remainder after 101 cents, what will 250 eggs Ans. 82.187. dividing the product of the second and third terms by the first, reduce 16. If a penny loaf weigh Goz it to the next lower denomination, when wheat is 6s 3d per bushel, and divide as before. what ought it to weigh when 7. A borrowed of B $250 for wheat is 8s 24d per bushel ? 7 months; afterwards B borrow Ans. 6oz isdrs. ed of A $300; how long must he 17. How many yards of flankeep it to balance the former nel 5qrs wide, will line 20 yards favori Ans. 5ms 25ds. of cloth 3qrs wide ? 8. If 100 men can do a piece Ans. 12 yards. of work in 12 days, how many 18. If a staff 4ft bin in length, men can do the same in 3 days? cast a shadow 6 feet, what istihe Ans. 400 men. height of a tree whose shadow 9. A goldsmith sold a tankard measures 108 feet ? weighing 39oz 15pwt for £10 Ans. 81 feet. 12s; what was it per ounce ? 19. If the earth revolve on its oz. pwt. axis 366 times in 365 days, in 39 15:10 12:: 1 Ans. 5s. 4d. what time does it perform one 11. If the interest of 8100 for revolution ? Ans. 23h 56m one year be 86, what will be the rev. ds. 4s nearly.* interest of 8336 for the same 366 : 365 ::1 tinte ? $ $ 20. If a person at the equator 100: 6:: 336 Ans. 820.16. be carried by the diurnal motion 11. If $100 gain 86 în one of the earth, 25000 miles in 24 year, in what time will a sum of hours, how far is he carried in a minute? money double at that rate, sim Ans. 1773 miles. ple interest? 21. There is a cistern which $ has three cocks; the first will 6:1:: 100 Ans. 16 yrs. empty it in $ of an hour, the 12. If 8100 gain 86 in 12 second in of an hour, and the months, in how many months will third in 1 hour ; in what time a sum of money double at that will they all empty it running torate, simple interest gether? h cis h cis Ans. 10m." 8 mo. 8 25:1::1:4 6:12;: 100 Ans. 200mo. .75:1::1:1.333 + 13. If $100 gain $6 in 365 1.50:1::1:0.666. days, in how many days will a money double at that rate, 6 cisterns. simple interest ? Ans. 6083 days. 6:60:31:10 Ans. rev. $ yr. sum of cism cism * This is called a sideral day. 22. Bought 4 bales of cloth, Ss. If my watch and seal be each containing 6 pieces, and worth 48 dollars, and my watch each piece containing 27 yards, be worth 5 times as much as my at £16 4s per piece ; what is the seal, what is the value of the value of the whole and the price watch? Ans. $40. per yard? 6 : 48 :: 5 Ans. €388 168 and 12s per yd. 23. If a hogshead, of rum cost 34. A cistern containing 230 875.60, how much water must be gallons, has two pipes; by one it added to it to reduce the price receives 50 gallons per hour, and to 1 dollar per gallon ? by the other discharges 35 gals. Ans. 12 gal. per hour; in what time will it be filled ? Ans. 15h. 20m. 24. If a board be 9 inches wide, how much in length will make a 35. If 40 rods in length and 4 square foot ? Ans. 16in. in breadth make one acre, how 9:144::1 many rods in breadth, that is 16 25. How many yards of paper i rods long, will make one acre ? 3 quarters of a yard wide, will Ans. 10 rods. pa er a room that is 24 yards 36. The earth is 360° in cir: round, and 4 yards high? Ans. 128 yards. cumference, and revolves on its axis in 24 hours; how far does a 26. The salary of the Presi- place move in one minute in lat. dent of the United States is 44o, a degree in that lat. being $25,000 a year; what is that per about 50 miles ? day? Ans. 868.493. Ans. 124 miles. 27. A garrison of 500 men has hm deg m provisions for 6 months; how 24 x 60 : 360 x 50 :: 1 many must depart that there may 37. If the earth perform its be provisions for those who re diurnal revolution in 24 hours, in main, 8 months ? Ans. 125. what time does a place on its sur28. If a man spend 75 cents face move through one degree ? per day, what does he spend per 360° : 24:: 1° Ans. 4 minutes. annum Ans. 8273,75. 29. If a field will feed 6 cows 38. There is a cistern which 91 days, how long will it feed 21 has a pipe that will empty it in Ans. 26 days. 6 hours ; how many such pipes will be required to empty it in 30. A lends B 866 for one 20 minutes ? year; how much ought B to lend A for 7 months, to balance the 39. What is the value of $642 favor ? Ans. $113.142. against an estate which can pay 31. At 81,25 per week, how only 69 cents on the dollar? many weeks' board can I have for Ans. $442,98. $100? Ans. 80 weeks. 40. How many men must be 32. What will 39 weeks' board employed to finish in 9 days, come to at $1,17 per week? what i5 would do in 30 days? Ans. $45,63 Ans. 50 men. m cows Ans. 18 pipes. OZ.. $ 75 RULE OF THREE IN VULGAR FRACTIONS. Prepare the fractions by reduction, if necessary, and state the question by the general rule; invert the first term, and then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator; the new pumerator, written over the new denominator, will be the answer required. Examples 1. If oz. cost £, what will 4. If my horse and chaise be loz. cost? worth $275, and the value of my oz. horse be that of my chaise, ş: 7 ::1 Then, what is the value of each ? 3x3x1=*£=£1 1s. 9fd. An. 1: ::} : $105 horse. 2. How much shalloon that is 1:47.5 :: 5 : $70 chaise. Ans. fyd. wide, will line 154 yards of 5. A lends B $48 for of a cloth that is 24 yard wide? year; how much must B lend A 131=* and 2={*:*::{ d's of a year to balance the favor? *x*Xf="990=44 yds. 6 in. Ans. $86.40. Ans. 3. If & gallon cost { £ what I sells of his share for £171; 6. A person owning of a farm will tuu cost? what is the whole farm worth? of is of į of }=1077 tun. Ans. £380. 2017 ::: Ans. £ 140. ASSESSMENT OF TAXES.* 1. Supposing the Legislature what part of it must a town pay, should grant a tax of $55000 to the inventory of which is $246007 be assessed on the inventory of Idol.inv. dol.tax. dol.jov. dol. all the rateable property in the 3000000 : 35000 :: 24600 : 287 Ans. State,which amounts to $3000000 * In assessing taxes, it is generally best, first to find what each dollar pays, and the product of each man's inventory, multiplied by this sum, will be the amount of his tax. In this case, the sum on the dollar, which is to be employed as a multiplier, must be expressed as a proper decimal of a dollar, and the product must be pointed according to the rule for the multiplication of decimals ; thus 2 cents must be written .02, 3 cents, 03, 4 cents, .04, &c. It is sometimes the practice to make a table by multiplying the value on the dollar by 1, 2, 3, 4, &c. as follows: TABLE. 100 is 3 00 200 6.00 9.00 400 12.00 500 15.00 600 18.00 700 21.00 800 24.00 900 27.00 10 100 3.00 1000 30.00 30 2. A certain school, consisting 4. The inventory of a certain of 60 scholars, is supported on school district is 84325, and the the polls of the scholars, and the sum to be raised on this inventoquarterly expense of the whole ry for the support of schools, is school is $75; what is that on $86.50; what is that on the dolthe scholar, and what does A pay lar, and what is C's tax, whose per quarter, who has 3 scholars ? | property inventories at 876.44 ? Ans. $1.25 on the scholar, and $4325 : 86.50 :: 1:.02cts. Ans. A pays 83.75 per quarter. and 76.44 X.02=$1.528 C's tax. 3. If a town, the inventory of 5. If a town, the inventory of which is $24600, pay $287, what which is $16436, pay a tax vf will A's tax be, the inventory of 8493.08, what is that on the dolwhose estate is $525.75 ? lar ? dol.inv, Tax. doliny. 24600.00 : 287 :: 525.75 : $6.133 $16436 : $493.08 ::1:.03cts. Ans. Ans. QUESTIONS. 1. How is the Single Rule of Three term contain different denomiknown? nations ? 2. By what other names is it some 8. Of what denomination will the times called ? quotient be? 3. Which of the given numbers is to 9. If the quotient be not of the be written down for the second denomination in which the anterm? swer is required, what is to be 4. How is it to be determined which done ? of the others is to possess the ! 10. How are two sums in Federal third place? Money, brought to the same de5. How do you proceed, after stat nomination ? (Ans. By annexing ing the question, to find the an ciphers.) 11. What is the method of proof in 6. If the first and third terms be of this rule ? different denominations, what is 12. How is the Rule of Three perto be done? formed in Vulgar Fractions ? 7. What is to be done, if the second This table is constructed on the supposition that the tax amounts to three cents on the dollar, as jn example 3d. USE.-- What is B's tax, whose rateable property is $276? By the table it appears that $200 pay $6, that $70 pay $2.10, and that $6 pay 18 cents. Thus $200 is $6 00 Proceed in the same way to find each indi70 2.10 vidual's tax, then add all the taxes together, 6 0.18 and if their amount agree with the whole gum proposed to be raised, the work is right. It is 276 $8.28 B's tax. sometimes best to assess the tax a trifle larger than the amount to be raised, to compensate for the loss of the fractions. 2. DOUBLE KULE OF THREE. The DOUBLE RULE OF THREE, sometimes called Compound Proportion, teaches to resolve such questions as require two or more statements in the Single Rule of Three. - In the Double Rule of Three, there are usually five numbers given to find a sixth, but there may be more, as seven or nine: Rule. 1. Make the number, which is of the same kind as the required answer, the second term. 2. Take any two of the remaining numbers that are of the same kind, and place one for a first term, the other for a third term, according to the directions given in the Single Rule of Three; then take any other two of the same kind, and place them in the same way, and so on, till all are used. 3. Multiply the product of the third terms by the second term, and divide the result by the product of the first terms, and the quotient will be the answer required. Examples. 1. A wall which is to be built to the height of 27 feet, was raised to the height of 9 feet by 12 men in 6 days; how many men must be employed to finish the wall in 4 days? 27-9=18 By taking 9 from 27, we find the wall is to be raised 18 feet higher, and it is required to know 9: 12 :: 18 how many men will finish it in 4 days; conse4 : 6 quently 12 must be made the second, term. Now if we take two numbers of the same kind, 36 108 viz. 9 and 18, it is plain that the 18'will require 12 more men than the 9, supposing the time to be the same; then 9 must stand in the first place, 36 ) 1296( 36 Ans. and 18 in the third. Again; if we take the 108 other two of the same kind, viz. the 6 and 4, and suppose the work the same, it is evident 216 that if the same work is required to be done in 216 less time, the number of men must be increased; i. e. if the work done by 12 men in 6 days is to be done in 4 days. more than 12 men must be employed; hence 6, must stand in the third place, and 4 in the first. 2. If a man travel 112 leagues in 29 days, when the days are 7 hours long, how far will he travel in 17 days, when they are i0 hours long? 29 : 112 : : 17 The days, their length being considered equal, would 7: : : 10 require the answer to be less than 112, because in this case he could not travel so far in 17 as in 29 days; and the hours, without regarding the days, would require the answer to be greater than 112, for he could certainly travel further in 10 than in 7 hours, and these two compounded as in the statement, give the distance required. : |