(15) A dealer bought two lots of snuff that together weighed 9 cwt. 3 qrs. 16 lb. for 971. 17s. 6d. Their difference in point of weight was 1 cwt. 2 qrs. 16 lb, and of price 81. 13s. 3d.. Their respective weights and values are required. (16) A father left among seven sons and a daughter an estate consisting of 10000l. in cash, with eight bills, each of 441. 10s. 6d. He ordered 361. to be bestowed upon his burial, and his debts to be paid, amounting to 2601. then his free estate to be divided in this manner, viz. the daughter to have the ninth part, and the seven sons to have equal shares. What is the daughter's part, and also what is the share of each son? QUESTIONS for Exercise at leisure Hours. (17) I would plant 2072 elms, in 14 rows, twenty-five feet asunder. How long must the grove be? (18) A brigade of horse, consisting of 384 men, is to be formed into a long square, having 32 men in front. How many ranks will there be? (19) Divide 1000 crowns betwixt A. B. and C. in such a manner that A. may have 129 more than B. and B. 178 less than C. (20) Part 2501. Give A. 37 more than B. and let C. have 28 fewer. (21) Six of the female cricketers that played lately in the Artillery-ground, fetched in company strokes as follow, viz, A. B. C. D. E. 207. A. C. D. E. F. 213. A. B. D. E. F. 189. A. B. C. E. F. 234. A. B. D. C. F. 222. B. C. D. E. F. 250. How many did they fetch on the other side, since these six persons wanted but fourscore and 13 notches to decide the game? (22) In order to raise a joint stock of 10000l. L. M. and N. together subscribed 8500l. and O. the rest. Now M. and N. are known together to have set their hands to 60501. and N. has been heard to say that he had undertaken for 4201. more than M. What did each proprietor advance? (23) There are two numbers, whose product is 1610; the greater is 46. What is their sum, difference, and quotas; what is the sum of their squares; and what is the cube of their difference? (24) There are other two numbers, the greater 7050, which, divided by the less, quotes 94. What is the difference of their squares? and what the square of the product of their sum and difference? (25) What difference will there be to the proprietors of an aqueduct, between doubling an expense, and halving a profit? (26) Part 1500 acres of land; give B. 72 more than A. and C. 112 more than B. (27) One of the smarts in the Accomptant's Office making his addresses in an old lady's family, who had five fine daughters, she told him their father had made a whimsical will, which might not soon be settled in Chancery; and till then he must refrain his visits. The young gentleman undertook to unravel the will, which imported that the first four of her girls' fortunes were together to make 25000l, the four last 330001. the three last with the first, 300007. the three first, with the last, were to make 28000l. and the two last with the two first 320001. "" Now, sir," said the old lady, "if you can make appear what each is to have, and as you like, seemingly, my third daughter, Charlotte, I am sure she will make you a good wife, and you are welcome." What was Miss Charlotte's fortune? (28) By selling 240 oranges at five for 2d. 120 of which cost me two a penny, and the other half three a penny, I evidently lose a groat. Pray how comes that about? (29) A. B. and C. play in concert at Hazard; and at making up accounts, it appears that A. and B. together brought off 137. 10s. B. and C. together 121, 126. and A. and C. together won 117. 16s. 6d. What did they severally get? (30) Four persons advanced in trade as follows, viz. W. X. and Y. raised 3501. 10s. W. X. and Z. 3447. 10s. X. Y. and Z. made up together 400l. and W, Y. and Z. contributed 3781. 4s. In the conclusion they parted with their joint property for 450 guineas. What did they gain or lose by their adventure? (31) A tradesman increased his estate annually a third part, abating 100%, which he usually spent in his family, and at the end of 3 years found that his net estate amounted to 31797. 11s. 8d. Pray what had he at first? (32) Ten pounds a quarter are allowed to five auditors of a fire-office. They attend about seven times in the quarter, and the absentees' money is always divided equally among such as do attend. A. and B. on these occasions never miss; C. and D. are generally twice in a quarter absent, and E. only once. At the payment, what has each man to receive? (33) Suppose a maid carrying apples to market were met by three boys, and that the first took half what she had, but returned ten; that the second took one-third, but returned two; lastly, the third took away half those she had left, but returned one, and when she had got clear she had 12 apples left. What number of apples had she at first? XI. REDUCTION. IN this and all the following rules, all great names are brought into small by Multiplication; on the contrary, all small names into great by Division. See Sect. VI. page 15. EXAMPLES in MONEY. (1) In 1307. how many shillings, pence, and farthings? (2) How many pence, shillings, and pounds, are in 24000 farthings? (3) In 80l. 15s. 11 d. how many farthings? (4) Reduce 16921 farthings to pounds. (5) Reduce 110l. Os. 64d. to halfpence. (6) How many pounds, &c. are there in 20553 halfpence? (7) In 1077. 10s. 8d. how many two-pences? (8) Reduce 5348 two-pences to pounds. (9) Reduce 67. 17s. to three-pences. (10) In 2782 three-pences, how many pounds, &c.? (11) In 10l. 10s. 8d. how many four-pences? (12) Reduce 38859 four-pences to pounds. (13) How many six-pences are there in 2001. 17s.? (14) Reduce 795 six-pences to pounds, &c. (15) In 21 guineas, how many shillings, pence, and farthings? (16) How many guineas in 24192 farthings? (17) In 12 moidores how many farthings? (18) How many moidores are there in 3240 pence ? (19) In 30l. how many crowns, half-crowns, and pence? (20) Reduce 20160 pence to half crowns, crowns, and pounds. (21) In 25 crowns, how many shillings, groats, and pence? (22) Reduce 25200 pence to groats, shillings, and crowns. (23) In 251. how many shillings, crowns, and pence? (24) How many shillings and pounds in 80 crowns? (25) How many crowns, half-crowns, and shillings, are in 2131. 15s. 6d. and of each an equal number? (26) In 120l. how many half-crowns, crowns, groats, and shillings? (27) In 36 crowns, as many half-crowns, shillings, and groats, how many pounds? (28) Reduce 470l. 178. to shillings and moidores. (29) Reduce 240 guineas to shillings, crowns, and pounds. (30) In 21 purses, each purse with 21 guineas, a crown, and a moidore in, what sterling do they contain? COINS. Case 1. To reduce Foreign and English coins to pounds sterling. RULE. Multiply the given number of pieces, by the shillings, sixpences, four-pences, three-pences, two-pences, pence, or halfpence, &c. that are in one piece; and the product will be accordingly either shillings, six-pences, &c. which bring into pounds sterling. EXAMPLES. (31) How many pounds sterling are there in 1178 dollars, at 4s. 3d. each? (32) In 470 pistoles, each 17s. 6d. how many pounds sterling? Case 2. To reduce pounds sterling into Foreign and English coin, &c. RULE. Reduce the given pounds sterling, and the given coin, into one name; that is, if you can reduce them both into shillings, six-pences, four-pences, or three-pences, &c. do so; then divide one by the other, and the quotient will be the answer. EXAMPLES. (33) A merchant is to pay 2491. 7s. 6d. With how many quarter-guineas can he do it? (34) In 3871. 18s. 4d. how many florins at 3s. 2d. each? Case 3. To reduce one kind of coin into another kind of coin. RULE. Reduce both coins into the same denomination, and then divide one by the other. EXAMPLES. (35) How many crowns of 5s. 4d. each, are in 474 pistoles of 18s. 6d. each? (36) How many guineas are equal in value to 1240 moidores? Of WEIGHTS and MEASURES. (1) In 14 lb. of silver, how many ounces, penny-weights, and grains? (2) How many lb. of silver are there in 138240 grains? (3) In 19 lb. 10 oz. 17 dwts. 22 grs. how many grains? (4) Reduce 74342 grs. to pounds. (5) In 4 ingots of silver, each weighing 4 lb. 6 oz. 22 grs. how many grains? (6) How many ingots, of 6 lb. 11 oz. 14 dwts. each, are there in 241056 grains? (7) How many lb. of silver are there in one dozen of dishes, each weighing 25 oz. 15 dwts. and one dozen of plates, each weighing 15 oz. 15 dwts. 22 grs. (s) A gentleman sent 455 oz. 1 dwt. 16 grs. of old plate, to his silversmith, with orders to make it into the following articles, viz. Punch bowls, each 24 oz. 4 dwts. Tan |