956. 3. At 50¢ each, the cost would be $8; at 1¢ apiece less, the cost is $8.00 --- $.16 = Ans. 4. (of 100 lb.) x 27 = 100 lb. x (of 27) = 100 lb. x 81 = 100 lb. X 2012 NOTE. — The 100 should not be used until the end; even then, 201 is changed to 2025 without thinking of multiplication, 1 being considered 25, and annexed to 20. See Art. 649. 6. 900 = 75 = (900 - 100) =(75 100) =9= 2. [($4.875 x 17350) = 196]+($4.9375 x 122.75] + [$.0825 x 2240 x 21]. 3. x - 470 x = 49739.55. 12. Duty=[B of (55¢ x 45 x 38)]+[20¢ x (45 x 38 x 4)]. 958. In multiplying by 427, the first figure of the product by 42 (7 x 6) is placed under the 2; in multiplying by 832, the first figure of the product by 8 is placed under the 8, and the first figure of the product by 32 (8 x 4) is placed under the 2. 959. These exercises contain some examples worked by short methods explained in previous chapters. See Arts. 650, 714, 791, 792, and 891. 960. See Arithmetic, Art. 384. 4. f is what per cent of ze? } is what per cent of ? is is what per cent of f? 5 is what per cent of 6? = 831%. 6. The deduction of the first discount leaves 80% of the list price; the deduction from this of 10% of itself leaves 90% of 80%, or 72% 7. One fills of tank in 1 hr., the other fills { in 1 hr.; both together fill 1 + in 1 hr., or +24, or 74; to fill 44 of tank, it will take 24 hr. = 7= 3 hr. 8. 6% for 60 da. = 80$; for 12 da., f of 80¢ or 16$; for 72 da., 80¢ + 16¢ = 964. Or, $ 4.80 for year, and ț of $4.80 for 72 da. 9. 16% = 2* ; 420 = 2; etc. 965. 5. Selling price = f of $1.50 = $1.127; gain = 224¢ = 1 of 90€. 6. Selling price =$9.60, a reduction of $2.40 from marked price, or } of $12, or 20%. 7. The rug is sold for $24. If this is of marked price, the latter is $30. 8. See 7. NOTE. — It is not to be expected that all the pupils' work will be shortened to this extent, but the majority of the class should be able to give answers at sight to these four examples. 9. Find t of £83 2s. 6d. by compound division ; do not reduce to pence. 966. 4. Let x = profits first year; then 220 = profits second year; x + 10 = 6970. 5. I wish to gain 15% of $.96, or $.14%, which makes my selling price $.96 +$.143 = $1.10%. Let x=marked price. 20. Or, writing all the foregoing in one equation : 7. The average pupil will be able to obtain the meanings of these terms by inquiries of his parents, friends, etc.; and he will remember much longer what he learns in this way, than if he finds the answer in the text-book. As the penalties for taking usurious interest vary in the different states, the teacher should ascertain the law of her own state in this matter. See Art. 1306. A tax bill or a policy of insurance brought in by a pupil and described, will add to the interest. The teacher should not spend too much time upon details that have no relevancy in her section of the country. Poll taxes, for instance, should not be dwelt upon in cities in which they are not collected ; etc. 9. The use of the hogshead as a measure of 63 gal. is fast becoming obsolete. The term “barrel,” to indicate 31į gal., is occasionally used in giving the capacity of large tanks, etc. The U.S. authorities require prices to be stated in the currency of the country from which the articles are exported; but as this would make the problem more complicated, the text-books generally give prices in U.S. money. No allowance is now made for leakage, the quantity actually imported being ascertained by measuring. 10. A port of entry is a place in which there is a custom house, established by the government. 967. 4. Any principal — $150, $575, or $343.75 — will double itself at 5% in (100 = 5) yr. 12. The pupils will need to obtain a correct idea of the meaning of the word “premium " in this connection, as they will find it used differently when they come to the study of Bonds and Stocks. The premium is the amount paid to the company assuming the risk. 968. 11. $ 3500 is raised on property worth $1750000; the rate is $3500 = $1750000 = 2 mills on $1. The man's property tax=2 mills x 24000 = $48; adding to this 1 poll tax, at $2, gives his total tax of $50. Ans. 969. 2. Multiply the denominators of the first and the third; divide the numerators of the second and the fourth. 5. While pupils in lower grades may be permitted to reduce both amounts to pence, it is now time to use a shorter method. The sums given may be changed to 384s. and 54s., or 1958. and 425. The arithmetical solution is apparent from the foregoing. The sides and the bottom contain 63 sq. yd., or 567 sq. ft. The bottom contains (18 x 15) sq. ft., or 270 sq. ft. The sides contain 567 sq. ft. — 270 sq. ft. = 297 sq. ft., which is the area of four rectangles, whose bases measure 18 ft., 15 ft., 18 ft., and 15 ft., respectively, the total being 66 ft. 297 -- 66 gives 44 as the number of feet in depth. 2. There are 4840 sq. yd. in an acre. (4840 x 3) = (1 of 242). Cancel. 3. The area of a trapezoid is found by multiplying one-half the sum of the parallel sides by the perpendicular distance between them. See diagrams, Arithmetic, Art. 929, Problems 6 and 9; and Art. 1265, Figs. 9 and 10. |