48. Suppose a servant is paid £8. 15s. 3d. for 7 months 3 weeks service, how much is that per year (365 days) ? Answer, £14. 14s. 9 d. 49. If Tea is sold at 7s. 9d. per pound, what is the price of 3 chests, weighing as follows:-No. 1, 3 Cwt. 1 qr. 20 lb. ; No. 2, 2 Cwt. 2 qro 14 lb. ; No. 3, 4 Cwt. O qr. 7 lb. ? Answer, £439. Os. 9d. 50. A person failing in business, pays 7s. 3d. in the pound; what must be received for a debt of £158. 13s. 9d. ? Answer, £57. 10s. 5 d. 51. How many Cwt. of Tobacco, at 2s. 10d. per lb., can be had for 32 guineas ? Answer, 2 Cwt. 13 lb. 52. Bought 13 Cwt. 1 qr. 15 lb. of Coffee for £180. 17s. 3}d. ; but 173 lb. being damaged, how must the remainder be sold per lb. so as not to lose by the accident ? Answer, 2s. 8 d. 53. If 1 Cwt. 3 qr. 18 lb. of Sugar cost £9s. 4s. 7}d., what quantity may be had for £473. 13s. 94d. ? Answer, 98 Cwt. 5 lb. 54. If 5 oz. 14 dwts. of Gold are sold for £25. 13s., what is the value of 10 lb. 5 oz. 13 dwts. 21 grs. ? Answer, £565. 12s. 5 d. 55. Suppose 10 lb. 5 oz. 13 dwts. 21 grs. cost £565. 12s. 5 d., what cost 5 oz. 14 dwts ? Answer, £25. 13s. 56. Bought 5 oz. 14 dwts. of Gold for £25. 13s. ; what quantity can I have for £565. 12s. 54d.? Answer, 10 lb. 5 oz. 13 dwts. 21 grs. 57. How many Cwt. of Sugar can be purchased for 35 guineas, at 9 d. per lb. ? 58. If 31 yards of Cloth were sold for 12s. 1}d., what would be the cost of 7 pieces, each 25% yards? 59. If a meadow maintain 21 cows for 15 days, how long would the same meadow keep 35 cows ? 60. A merchant bought 4 hogsheads of Sugar, weighing as follows: No. 1, 3 Cwt. 2 qrs. 12 lb.; No. 2, 2 Cwt. 0 qr. 25 lb. ; No. 3, 4 Cwt. 3 qrs. 15 ]b.; No. 4, 3 Cwt. 1 qr. 19 lb. ; at the rate of £2. 11s. 74• per Cwt. Required the value of the whole ? COMPOUND PROPORTION Is a Rule by which the student may resolve such questions as require two or more statings in Simple Proportion.* Erample. If 7 men in 12 days reap 126 acres, in how many days will 16 men reap 72 acres? The Answer must be days; consequently, days must be noticed in both statings. 1st. If 7 men in 12 days reap acres, in how many days will Here, by Rule 2d in Simple Proportion, the less number (7) is put in the second term, because 16 men could reap a certain number of acres in less time than 7 men could : thus, 16 men : 7 men :: 12 days. 2d. If - men in 12 days reap 126 acres, in how many days will men reap 72 acres ? Here again the less number (72) is put in the second term, because 72 acres could be reaped by a certain number of men in less time than 126 acres could :--thus, 126 acres : 72 acres :: 12 days. Now, combining the statings, 16 men : 7 men 126 acres : 72 acres :} 12 days. :: By Rule 4th, Simple Proportion, multiply the second and third terms together, and divide by the first. * The method of reasoning in the Examples is the same as pursued in Simple Proportion. It may be proper to remark, each Example is divided into two parts, only to render the reasoning plainer. In performing the Exercises, the learner may dispense with this in placing the terms. persons 18 persons Answer, 3 days. Example. If a family of 8 persons expend £200 in 9 months, how much will serve a family of 18 people 12 months ? The Answer must be money; consequently, money must be noticed in both statings. 1st. If a family of 8 persons expend £200 in months, how much will serve a family of 18 people - months ? Here, the greater (18) is put for the 2d term, because 18 persons will spend more money in a certain number of months than 8 persons will;—thus, £200 or, dividing by 2, 4 persons 9 persons £200 2d. If a family of persons expend £200 in 9 months, how much will serve a family of people 12 months ? Again, the greater (12) is put for the second term, because a certain number of persons will spend more in 12 than in 9 months: thus, 9 months 12 months £200 dividing by 3, 3 months 4 months €200 Combining these statings 1st, 4 persons 9 persons 2d, 3 months : 4 months 3 LGCO } £200 Example. If the carriage of 11 Cwt. 2 qrs. for 150 miles cost £6. 14s. 8d., how much must be paid for the carriage of 15 Cwt. 1 qr. 22 lb. for 64 miles at the same rate ? The Answer must be money, consequently, money must be noticed in both statings. 1st. If the carriage of 11 Cwt. 2 qrs. for miles cost €6. 14s. 8d., how much must be paid for the carriage of 15 Cwt. 1 qr. 22 lb. for miles at the same rate ? Here, the greater (15 Cwt. 1 qr. 22 lb.) is put for the 2d term, because the carriage of 15 Cwt. 1 qr. 22 lb. for a certain distance would cost more than the carriage of 11 Cwt. 2 qrs.; .;-thus, : 15 Cwt. 1 qr. 22 lb. : £6. 14s. 8d. or, 1288 lb. 1730 lb. 2d. If the carriage of Cwt. &c. for 150 miles cost £6. 14s. 8d., how much must be paid for the carriage of Cwt. &c. for 64 miles at the same rate ? 11 Cwt. 2 qrs. 1616 pence. Here the less (64) is put for the 2d term, because the carriage of a certain weight 64 miles, would cost less than the carriage of the same weight 150 miles :-thus, 150 miles : 64 miles :: 1616d. (£6. 14s. 8d.) Combining the statings, 1st, 1288 lb. 1730 lb. 2d, 150 miles 64 miles Multiply the 2d and 3d terms together, and divide by the 1st. 1288 lst term. 1730 2d term. 150 Ist term. 64 2d term. 1616 pence. EXERCISES. 1. If 27 shillings be the wages of 4 men for 7 days, what will be the wages of 14 men for 10 days? Answer, £6. 15s. 2. If 2 acres of land will maintain 3 horses for 4 days, how long will 5 acres of the same pasture maintain 6 horses ? Answer, 5 days. 3. Suppose £100 in 12 months gain £6 interest, how much will £75 gain in 9 months ? Answer, £3. 7s. 6d. 4. If 12 men consume 32 pounds of bread in 18 days, how much will 24 men consume in 36 days? Answer, 128 lb. 5. How many men can complete a trench of 135 yards long in 8 days, when 16 men can dig 54 yards of the same trench in 6 days? Answer, 30 men. 6. If the carriage of 126 lbs. for 100 miles cost 6 shillings, how many pounds can I have carried 750 miles for a guinea ? Answer, 58 lbs. 7. How many bushels of Oats will be sufficient for 20 horses 24 days, if 14 horses eat 56 bushels in 16 days? Answer, 120 bushels. 8. If a footman travel 130 miles in 3 days, when the days are 12 hours long; in how many days, of 10 hours each, will he travel 360 miles ? Answer, 9% 3 days. 9. If 2 men in 3 days can earn 15 shillings, how much can 7 men earn in 4 days? Answer, £3. 10s. 10. What principal will gain £20 interest in 19 months, if £100 gain £4 interest in 12 months ? Answer, £315. 15s. 9fd. 11. If a barrel of beer he sufficient to last a family of 8 persons 12 days, how many barrels will be drank by 16 persons in a year? Answer, 60% barrels. 12. If a regiment of soldiers, consisting of 939 men, consume 351 quarters of Wheat in 168 days, how many soldiers will consume 1404 quarters in 56 days? Answer, 11268 soldiers. 13. If 8 men in 14 days can mow 112 acres of grass, how many men must be employed to mow 200 acres in 10 days? 14. If 9 men cast 30 yards of ditching in 12 days, working 8 hours a-day, how many men will cast 45 yards in 18 days, working 6 hours per day? |