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Feb. 9, 6
June 11, 27

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£182 8 41

J. ROBINSON Dr. to H. WILSON.

lbs. beef, at 11 d. per lb.
lbs. mutton, at 10 d. per lb.
stone lard, at 3s. 111⁄2d. per stone.
lbs. suet, at 9 d. per

lb.

lbs. beef, at 11 d. per lb.
lbs. mutton, at 10 d. per lb.

July 17, 34 lbs. fat, at 44d. per lb.

Aug. 16, 28 lbs. pork, at 9 d. per lb.

Sept. 11, 14 lbs. mutton, at 10 d. per lb.

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Make out this bill of parcels, and show how it should be receipted. How much change will there be out of a £10 note:-16 cwt., at 13d. per cwt..; 4 OZ., at 3s. 2d. per oz.; 10 yds., at 2s. 3d. per yd.; 131⁄2 lbs., at 7d. per lb.; 31⁄2 dozen, at 9d. per dozen. Answer,

£6 17s. Od.

Write the following account as a bill, and find the amount: 3 lbs. of coffee, at 20d.; 2 lbs. of tea, at 4s. 6d.; 12 lbs. of moist sugar, at 5 d.; 10 lbs. of rice, at 3d.; 8 lbs. of loaf sugar, at 74d.; 9 lbs. of raisins, at 61d.; 7 lbs. of currants, at 5 d. Ans. £1 15s. 8d.

Make out and add up the following bill of parcels: 4 yds. cloth, at 12s. 6d.; 12 yds. velvet, at 8s. 3d.; 15 yds. cambric, at 5s. 4d.; 24 towels, at 2s. 3d.; 14 yds. serge, at ls. 7d.; 35 yds. cambric, at 1s. 1d.; 18 vds. silk, at 12s. 3d.; 5 pairs stockings, at 2s. 2d. ; 48 pairs gloves, at 1s. 3d.; 12 yds. velvet, at 3s. 6d.; 2 cloaks, at 63s.; 6 pairs gloves, at 2s. 6d. Answer,

£40 18s. 101⁄2d.

Make out the following bill, and add up: 27 quires of paper, at 3s. 9d.; 75 reams ditto, at 1s. 7d.; 36 quires ditto, at 1s. 8d.; 15 reams, at 11s. 6d.; 17 reams, at 10s. 7d.; and 120 vols. of poems, at ls. 24d. Ans. £38 17s. 5d.

Make out a bill with the following items:-67 yds. of print, at 3d.; 63 yds. dimity, at 63d.; 23 yds. calico, at 7 d.; 79 yds. flannel, at 1s. 11d.; 33 yds. cloth, at 5s. 6d.; 79 yds. silk, at 4s. 7d.; 397 yds. of sheeting, at ls. 11d.; 72 yds. of towelling, at 7d.; 73 yds. of lace, at 3s. 11d.; 94 yds. of curtains, at 3s. 74d.; 63 yds. of damask, at 6s. 74d; 251 yds. damask, at 2s. 11d. Ans. £246 2s. 9d.

In this sum the cost of the separate items was19s. 8d.; £115s. 6d. +2; 15s. 4d.; £7 16s. 2d. +; £9 5s. 7 d.; £18 6s. 6d. +; £38 17s. 5d.; £2 6s. 7 d. +3; £14 10s. 114d.; £126 12s. 04d.+1; £21 2s. Od.+; £3 14s. 8d. +1.

Make out a bill with the following items:-19 yds. damask, at ls. 10d.; 18 yds. serge, at 3s. 94d.; 12 yds. dimity, at 4s. 8d.; 6 yds. sheeting, at 2s. 9d.;

15 yds. towelling, at 74d.; 24 yds. calico, at 81d. : 791⁄2 yds. cloth, at 4s. 6d. ; 24 yds. sheeting, at 6s. 6d.; 31 pairs gloves, at 1s. 11d.; 44 hanks of thread, at 23d.; 64 dozen of tape, at 24d. per doz.; 67 reels cotton, at lid.; 74 yds. tape, at 11⁄2d.; 31⁄2 doz. laces, at 1d. each; 74 doz. tape, at 31⁄2d. per dozen. £43 6s. 5d.

Ans.

PROPORTION-SIMPLE.

1. If 5 horses cost £4 13s. 4d., how many can be bought for £70 10s. 6d.

Here the unknown quantity is the number of horses that can be bought for £70 10s. 6d. Call this, and let it form the fourth term of a proportion. If this number is to be greater than 5, the ratio will be an increasing one from 5:2, therefore the remaining two terms must be arranged in an increasing order from small to greater, as £4 13 4:£70 10 6. If ∞, on the contrary, is to be less than 5, the remaining terms must be arranged in a decreasing ratio, from greater to less, £70 10 6:£4 13 4. The proportion thus stands £4 13 4:£70 10 6::5:x.

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(1) £39 11s. 8d. is the poor-rate on £791 13s. 4d., what is the rate on £191 1s. 7d. Ans. £9 11s. 08d. (2) If 108 men can do a piece of work in 532 days, how many men will do it in 336 days? Ans. 171. (3) If 8 yards of cloth cost £11 8s. 9d., what will 40 yards cost? Ans. £26 18s. 214d.

(4) If 98 gallons of wine cost £14 16s., what will 105 gallons cost? Ans. £15 17s. 1 d.

(5) What is the rent of 547 acres of land, at 15s. 6d. per acre per annum? Ans. £423 18s. 6d. (6) If 14 gallons of wine cost £9 12s., what will 75 cost? Ans. £51 8s. 6d. +6.

(7) A man's income is £1000 per annum, he spends £1 18s. 8d. per diem, what is his saving. Ans. £294 6s. 8d.

(8) Bought coffee at 1s. 3d. per lb., what did 25cwt. 3qrs. 14lbs. cost? Ans. £187 3s. 3d.

(9) If I lend £180 for 16 months, how long ought I to borrow in return £240 10s? Ans. 11 months 3 weeks 61 days.

481

(10) If 42 masons can build 180 yards per hour, how many would do the same in 20 min.? Ans. 126. (11) What is the property tax on £545 0s. 8d., at 1s. 4d. per £? Ans. £36 6s. 8d. +15. (12) How many yards of paper paper 210 square yards? Ans. 280.

yd. wide will

qr.

14 lbs.,

Ans. 3

(13) If for £15 I have carried 5 cwt. 1 321f., how far can I have 2 tons carried? miles 1 furlongs.

In all cases of simple proportion, or single rule of 2nd term x 3rd term

three, the answer x =

1st term

can be

deduced from 1st principles by the use of multiplication and division only. Thus take Ex. 2.

If 108 men can do a piece of work in 532 days, how many men will do it in 336 days?

Statement:

Men required to do the work in 532 days=108

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1 day 108 × 532 336 days 108 x 532_ =171

336

Work out the following examples on 1st Principles. 1. A man's income was £1000 in the year 1863, his savings £397 15s. Od., what did he spend daily? Ans. £1 13s. Od.

2. How much gin at 8s. 2d. per gal. may be had for 84 lbs. chocolate, at 3s. 21d. per lb? Ans. 33 gals. 3. How much does a bankrupt pay on £2735 at 11s. 7 d. in the £ ? Ans. £1589 14s. 4d.

4. How much sago can be bought for £1000 10s. if 10 qrs. 191bs. cost 34s. 8d. Ans. 6156 qrs. 11 lbs.

5. What length should a garden have which is 189 ft. wide to be equal to one 120 yds. wide and 144 yds. long? Ans. 274 yds. 10 in.

6. What is the loss on £20 8s. at 1d. in the shilling? Ans. £2 2s. 6d.

7. If 81 gallons of spirits cost £12 17s. Od., what will 243 gals. cost? Ans. £38 11s. Od.

8. If 21 tons of coal cost £12 15s. Od., what will 14 tons cost? Ans. £8 10s. Od.

9. If 14 tons of coal cost £8 10s. Od., what will 21 tons cost? Ans. £12 15s. Od.

10. If 547 acres of land are rented for £423 18s. 6d., what is that per acre? Ans. 15s. 6d.

11. If 75 yards of silk cost £17 9s. Od., what will 25 yards cost? Ans. £5 16s. 4d.

12. If a tax be 1s. 4d. in the £, what is it in £272 10s. 4d. ? Ans. £18 3s 41d.

13. If £67 10s. 6d. be the interest on £6879 16s. 7d. for 11 months, what principal will gain £27 13s. 2d. in the same time? Ans. £2817 19s. 9d. +

14. If 64 men build a house in 79 days, how long will 37 men be building it? Ans. 13634 days.

15. Laid out £37 16s. 7d. in iron, at the rate of 1 cwt. 3 qrs. for £17 2s. 6d., how much shall I get? Ans. 3 cwt. 3 qrs. 1210 lbs.

2055

16. How many casks of raisins, each weighing 7cwt., can I purchase for £72 12s. 6d., at £7 9s. 6d. for 11 cwt. ? Ans. 15 casks +1261 cwt.

29

17. How much coal, at 17s. for 1 ton 3 cwt., can I purchase for £16 7s. 9d.? Ans. 22 tons 32% cwt.

18. The expenses of a parish are £879 16s. 7d., and the rental is £87967 16s., how much in the £ must be levied to pay them? Ans. 2d. +

19. If I spend £7 16s. 7d. per day, how much can I save out of an annual income of £8796 16s. 7d.? Ans. £5939 3s. 8d.

20. If it takes a man 17 hours 20 min. to accomplish a journey, travelling at the rate of 17 miles per hour, what time will it take him at the rate of 16 mil s per hour? Ans. 18 hrs. 23 min. 1 sec.

21. A garrison has provision for 25,500 men for 6 months, how many will it provision for 11 months? Ans. 13909 men.

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