(14) If I save £2. 12s. 6d. a month, how long will it take me to accumulate £25 ? (15) Out of £18. 4s. 9d. I bought as many sheep as I could at £1. 15s. 6d. each, and with the remainder I bought a lamb. Find the cost of the lamb. (16) Out of £13. 138. I bought as many articles as I could at £1. 10s. each. How much more money shall I want to buy one more article? (17) How many months of 28 days each are there in a year? (18) If I start Oct. 4th and travel 85 miles a-day, on what day shall I reach a place 450 miles off? (19) How many periods of 12 minutes are there in 1 hour? (20) To how many persons can I give £68. 14s. 10d. if I have £600 ? 4. If 1 article costs 4s. 7d., how many can I buy for £28,450 ? On trial it would be found that the process employed above would be so long as to be practically useless. Some artifice for contracting the operation is therefore indispensable. (See Ch. IV. § 7.) Make a table as follows: By means of this table we see that we can buy 100,000 articles, and shall yet have some money remaining. The table further shews us that with this remainder we can pay not only for 10,000, but for twice 10,000, or 20,000 articles. 20,000 articles cost 2 × £2291. 13s. 4d. £4583. 6s. 8d. = £5533 6 8=1st remainder 4583 6 8=cost of 20,000 articles With this second remainder we cannot buy another 10,000, but we can buy much more than 1000 articles, and the question arises : How many thousands? 1000 articles cost, by the table, £229. 3s. 4d. To make a rough guess as to the number of times this is contained in the second remainder, £950, we should examine the figures of highest value in each, which are respectively 2 hundreds and 9 hundreds; this leads us to suppose that we can pay for 4 thousands. On trial we find that 4 × £229. 3s. 4d. = £916. 13s. 4d. 3rd remainder £950 0 0=2nd remainder 916 13 4= cost of 4000 articles 33 6 8 With this third remainder we can pay for 100 articles. 4th remainder £33 6 8=3rd remainder 22.18 4 cost of 100 articles 10 4 = With this fourth remainder we can buy 4 × 10 articles. £2. 5s. 10d. = £9. 3s. 4d. 4 x £10 8 4= 4th remainder 5th remainder 0 With this fifth remainder we can buy 5 articles. £1. 2s. 11d. £1 5 0=5th remainder Consequently we can pay for 124,145 articles, and shall have 2s. 1d. over, which will not pay for another article. EXERCISE XX. (1) How many times are £5. 18s. 7d. contained in £800. 8s. 9d.? (2) How many articles can I buy for £2118. 18s. 3d. if each costs £9. 15s. 3d.? (3) By what number must I multiply £15. 13s. 7d. to obtain £4280. 88. 3d. for product? (4) £4973. 11s. 2d. ÷ £30. 17s. 10d. (5) If I put by £91. 7s. a-year, how long shall I take to accumulate £1370. 5s. ? (6) I invest £9287. 10s. in railway shares, each costing £92. 17s. 6d. and yielding a yearly income of £3. 10s. each. Find my total yearly revenue. (7) How many Napoleons at 15s. 9d. each can I get for 189 Prussian thalers at 2s. 10d. each? (8) (227 × £16. 11s. 4d.) (28 x 18s. 11d.). (9) How many guineas are there in £510. 6s.? (10) A earns £9. 2s. 6d. a-week, and spends £7. 5s. a-week. How long will he be in saving £150? (11) A man's wages are £1. 17s. 6d. a-week; his wife earns 18s. a-week; his 2 sons earn 6s. 9d. a-week each. How long must the wages of the family remain unpaid to amount to £79. 7s. ? (12) How many sovereigns, half-sovereigns, crowns, half-crowns, florins, shillings, sixpences, fourpenny-pieces, threepenny-pieces, pennies, halfpennies, and farthings, an equal number of each, can be got from £358. 17s. 5d.? (13) How many times are £3. 18s. 10d. contained in £429. 11s. 3d.? (14) £5327. 3s. 5d. ÷ £6. 13s. 2d. (15) A man's income is £2. 7s. 6d. a-week, and his expenditure, on an average, £3. 1s. 10d., but he has £50 to begin with. How much a-week does he spend more than he gets? How many weeks will the £50 keep him out of debt? And how much will he be in debt after 100 weeks from the commencement? (16) A certain book cost 7ąd. per copy for the paper, 44d. for the printing, 5d. for the binding. The total issue cost £110. 188. 9d. Of how many copies did it consist? And what was the profit on the whole issue if each copy was sold for 2s.? (17) An omnibus costs to work, 5s. 6d. a-day for the driver, 5s. a-day for the conductor, 8s. 6d. a-week for the keep of each of 8 horses, 6s. 9d. a-week for sundries. These omnibuses run on Sundays. If the weekly expenses amount to £333. 11s. 3d., how many omnibuses are there at work? (18) How many times can we subtract £1. 3s. 7 d. from £78,492, and what will be over? (19) If I have £18. 11s. 9d., and buy as many books as I can at 5s. 3d. each, and with the remainder buy a slate, what did it cost? (20) With an inheritance of £12,700, I bought as many shares at £92. 7s. 6d. as I could get. How many shares at £1. 9s. 9d. can I buy with the remainder? (21) How many times must £3.5s. 84d. be added to £562. 12s. 11d. to make £14,000 ? (22) Find my income if my income-tax at 7d. in £1 amounts to £14. 2s. 11d.? (23) How many Napoleons at 14s. 114d. each are equal to 718 Prussian thalers at 2s. 103d. each? (24) How many pounds of tea at 2s. 8d. per lb. must be given in exchange for 112 lbs. of coffee at 1s. 2d. per lb., and 88 lbs. of raw sugar at 4d. per lb. ? (35) £734. 8s. 2d. ÷ £7. 1s. 14d. (37) £154. 108.48. 3 d. CHAPTER VIII. DIVISION (continued). 1. Distribute £9. 12s. 6d. equally among 3 persons. I will each have? How much The £9 will give £3 each, the 12s. will give 4s. each, and the 6d. will give 2d. each; therefore each person will have £3. 4s. 2d. This question is indicated thus: £9. 12s. 6d. ÷ 3. The symbol (÷) has thus a perfectly new interpretation, viz., the distribution of a given quantity into so many equal parts. Learn by heart: This sign (÷) is called DIVIDED BY, and bears TWO interpretations; 1st. HOW MANY TIMES is the QUANTITY following the sign contained in the quantity preceding the sign, and the answer will be so MANY TIMES; 2nd. Distribute the quantity before the sign into as many equal parts as is indicated by the NUMBER after the sign, and the answer will be sO MUCH TO EACH PART. 2. Divide £357. 3s. 8d. between 2 persons. Dividing first the 3 hundred-pound notes, each person would receive 1 hundred-pound note, and there would be 1 hundred-pound note over; this we convert into 10 ten-pound notes, which, with the 5 ten-pound notes we have already, make 15 ten-pound notes, and these, divided among the 2 persons, give 7 ten-pound notes to each, and 1 ten-pound note over; converting this into 10 pounds, and adding the 7 pounds we have already, we have 17 pounds, of which we can give 8 pounds to each of the 2 persons, leaving 1 pound over; convert this into 2 half-sovereigns, and give 1 half-sovereign to each; now divide the 3 shillings, giving 1 shilling to each, and convert the 1 shilling over into 12 pence, which, with the 8 pence, give 20 pence, of which each person will have 10 pence. Total to each person, £178. 11s. 10d. £. s. d. 2) 357 3 8 Wording: 2 in 3, 1′, carry 1; in 15, 7'′, carry 1; in 17, 8', carry 1 (pound) = 2 half-sovs.; in 2, 1'; in 3, 1', carry 1 (shilling) = 12 pence; in 20, 10'. Ans. £178. 11s. 10d. Divide £743. 178. 81d. among 3 persons. £. s. d. 3) 743 17 84 £247 19 2 Wording: 3 in 7, 2′, carry 1; in 14, 4′, carry 2; in 23, 7', carry 2; in 5, 1', carry 2; in 27, 9'; in 8, 2', carry 2; in 9, 3'. Ans. £247. 19s. 2 d. |