if it consists of pounds, ounces, &c. it will be most convenient to reduce the pounds to ounces, and proceed by Rule 2. What is the value of 3610 of gold, at £64 per i? 36 x 64 = £2304 Anf. Prob. 2. To ascertain the value of any given quantity of gold in Spanisis milled Dollars. THEOREM 2. Ipwt. of gold = 515. I dol. = 6s. And 5==, therefore, Sa Rule: Reduce the given quantity of gold to penny. weights; then, as the denominator is to the given quantity, so is the numerator to the answer in dollars. Or, Divide by the denominator, and multiply the quotient by the numerator. Or, Divide by the denominator, and subtract the quotient from the dividend ; in either case you will have the anfwer. 1. What is the value of 6oz. 6pwt. of gold, in Spanish dollars ? 60%. Opwt. 20 126 pwt. pwt. As 9 : 126 :: 8 8 Or, Or, 9)126 9) 126 91008 Subt. 14 14x8 = 112 Ans: Anf. 112 dollars. 112 Ans. PROB. 3. To ascertain the weight of gold equivalent to any given sum, currency. Rule 1.-If the given fum be in pence, reverse Rule 1, Theor. 1, that is ; As the numerator 8 is to the given sum in pence ; fo is the denominator 3 to the weight required in grains. What What weight of gold is equal to 45. ? d. 3 12 48d. 8)144 Anf. 18 grains. RULE 2.--If the given sum be in pounds, shillings and pence ; As 5} is equal to 1° ; therefore divide the given sum by 8, and that quotient by 2 ; add the two quo. tients together, double the last denomination, and you will have the answer. What quantity of gold is equivalent to 45 135. 4d. ? Oz. paut. gr. Mark the pounds, shillings 8)45 13 4 and pence, as 0%. pwr. & gr. S 2)5 14 Add. 17 2 II 0%. 8 6 Ans. PROB. 4. To find the weight of gold equivalent to any giv en number of dollars, RULE.-Divide the dollars by the numerator 8, add the quotient to the dividend, and the sum is pennyweights. Required the weight of gold equal to 76 dollars? 76+8 = 91 and 76+91= 85pwt. Ans. RULE OF THREE DIRECT, IN DECIMALS. RULE.-Having reduced your fractions to decimals, and stated your question as in whole numbers, multiply the second and third together ; divide by the first, and the quotient will be the answer. 1. If of a yard cost az of a pound ; what will 9 yards come to ? Z ,625, '= ,583 4- and } =,666+ .. rd. As ,625 :,583 :: 9,666 ,583 28998 27328 48330 ,625)5,635278(9,0164+ = £9 os. 31d. Ans. 2. If 10%. of silver coit 6s. 8d. what is the price of a bowl, which weighs 1tb 70%. 13gr. ? Anf. £6 6s. 10d. 3. If 9 yards coft £6 3 75. 6. ; what will { yard come to ? Anf. 35. 5 d. 4. There is a ciltern which has three cocks, the first will empty it in of an hour, the second in 1, and the third in 1 hour ; In what time will it be emptied, if all three run together? b. Cil. h. CiA. Cift. h. Cit. ,25:11:1:4 As 6:1::1.:,1666+ = As ;1:1,333 + (10 min. Ans. 1,5 : 1:: 1:0,666+ 6 cistern. 5. A conduit has a cock, which, running into a ciftern will fill it in 12 minutes : This cistern has 3 cocks ; the first will empty it in iš hour, the second in 37 min. utes, and the third in an hour ; In what time will the ciltern be filled, if all four run together? b. C. 6. Cit, :1:0,8 As 4,4 do. emptied in do. ,62.5 : :: 1:1,6% emptying do. ,6 cistern difference. 25:1:: 1:2 1,25 : 1 } h. m. Cift. h. Cift. h. Then, as ,5 : 1 :: 1:1,66+ = 1 40 Ans. The following Questions are in the Coin of the United States. 6. If 19 yards coft 25dol. 7d. 56. ; what will 4351 yards come to ? rds, dol. d. c. Yds. As 19:25,7 5:: 435,5 25,75 21775 30485 21775 8710 D. d.c.m. 19)112 14,125(590,2 1 7o Anj. 7. If 345 yards of tape cost 5dol. id. 76. 5m. ; what will one yard cost ? rds. D. d. c. m. rd. As 345 : 5, I 7 5 : I d. c.m. 345)5, I 7 50,0 I 5. 3 4 5 : I 1 7 2 5 I 7 2 5 * 8. If I give 12 dol. 8d. 26. 5m. for 675 tops ; how many tops will 19 mills buy? D. d. c. m. T. d. C. m. As 12, 82 5:675 :: 20 I 9 ,019 6075 675 12,825) 12,825(1 top, Answero 12,825 RECIPROCAL PROPORTION, OR, RULE OF THREE INVERSE, Teaches, by having three numbers given, to find a fourth, which shall have the fame proportion to the second, as the first has to the third. Therefore, the greater the third term is, in respect to the first, the less will the fourth term be in respect to the - second ; or, the less the third term is in proportion to the firít, the greater the fourth must be in proportion to the fecond ; and this is called reciprocal, inverted or indired Proportion. The principal difficulty, that will embarrass the learner, will be, to distinguish when the proportion is direct, and when indirect.--This is done by an attentive confideration of the sense and tenor of the question proposed : For if thereby it appears, that when the third term of the ftating is less than the first, the answer must be less than the second ; or when the third is greater than the first, the answer must be greater than the fecond ; then the proportion is direct : But, if the third be less than the first, and yet the sense of the question requires the fourh to be greater than the second ; or if the third being greater than the first, the answer must be less than the second, the proportion is inverse, RULE.--* State and reduce the terms as in the Ri of Three direct ; then, multiply the firit and second terms * If 4 men can do a piece of work in 12 days ; in what time wil 8 men do it? 4 X 12 As 4 nien : 12 days :: 8 men : =6 days, the answer. 8 And here the product of the first and second terms, that is 4 times 12, or 48, is evidently the time in which one man would perform the work ; therefore, & men will do it in one eighth part of the habe, w 6 days. |