34. Bought 18 pieces of Cloth, each containing 27 yards, at the rate of 4s. 11d. per yard. Required the value of the whole?

Answer, £119. 9s. 6d.

35. If a certain number of men can raise a wall in 10 days, when they work 12 hours a-day, how many days would the same wall require in building, if the men worked 8 hours?

36. If £5. 3s. 9d. is paid for 23 yds.

English, 1 qr. ?

Answer, 15.

qrs., what cost 137 ells

Answer, £37. 9s. 2d.

37. How much do I spend yearly, if I spend 17s. 6d. per day?

38. How many yards of Stuff, 3 yards to a piece 17 yards long, and 2 wide?

Answer, £320. 2s. 8d.

wide, are equal in length

Answer, 10 yds. 3 nls.

39. What cost 42 qrs. 3 bus. of Wheat, at £1. 9s. 6d. per quarter? Answer, £62. 10s. 0 d.

40. If a wall 7 ft. 8 in. high, cast a shadow which is 5 ft. 4 in. in length, required the height of a steeple casting a shadow 138 ft. 7 in. in length? Answer, 199 ft. 2 in.

41. Bought 3 tuns of Oil for £195. 17s. 6d.; but 75 gallons being damaged, I am willing to sell the remainder at a certain price per gallon, so as neither to lose nor gain by the sale.

selling price per gallon?

Required the Answer, 5s. 9d.

42. How much Chocolate, at 3s. 8d. per lb., can I have for 12 Cwt. 1 qr. 4 lb. of Rice, at 5 d. per lb. ?

Answer, 1 Cwt. 1 qr. 24 lb.

43. Paid 17s. 9d. for 7 yards of Linen; what must be given for

5 pieces, each containing 27 yards?

Answer, £17. 8s. 7 d.

44. How many pieces of Coin of 7s. 3d. in value, are equal to 1172 pieces of 4s. 8d. in value? Answer, 761 pieces. +11d. 45. A merchant failing in business, owes £3726. 15s. 9d.; but his effects amount only to £848. 7s. 1d.; what must his creditors receive per pound? Answer, 4s. 6d. 46. Purchased 17 pieces of old Lead, each weighing 1 Cwt. 2 qrs. 13 lb., at 9s. 8d. per Cwt: required the value?

Answer, £13. 6s. 8d.

47. If 1 ounce of Coffee cost 2 d., what quantity can be had for

£13. 5s.?

Answer, 88 lb. 5 oz.

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. 94d.

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 qr 14 lb.; No. 3, 4 Cwt. 0 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. 31d.; but 173 lb. being damaged, how must the remainder be sold per lb. so as not to lose by the accident? Answer, 2s. 8d.

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. 51d., 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 94d. per lb. ?

58. If 3 yards of Cloth were sold for 12s. 11⁄2d., 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 lb.; No. 4, 3 Cwt. 1 qr. 19 lb.; at the rate of £2. 11s. 7d 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.*

Example. 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

16 men reap

acres?

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,

2d. If

16 men : 7 men :: 12 days.

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.

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.

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 much will serve a family of 18 people

months?

months, how

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,

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,

Multiply the 2d and 3d terms together, and divide by the 1st.

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. qr. 22 lb. for a certain distance would cost more than the carriage of 11 Cwt. 2 qrs. ;-thus,

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,

Multiply the 2d and 3d terms together, and divide by the 1st.