1084. 2. There are 5280 ft. in a mile. 5280 × 176 ÷ 3520 = number of minutes. Cancel. 000 32 3. 1875 A.=$9; 1A.= $9 ÷ 18750-$9×19900; A. = $9×18000 x 375 Cancel. 11. .625+.4375+.75+.09375+2.46=312.52. 12. 142.50 ÷ (5.25 — 4.95) = number of tons, 475. Total 14. The distance traveled in 1 revolution is 13 ft., the circumference of the wheel. 15. Three hundred forty-nine thousandths; three hundred (units) and forty-nine thousandths; three hundred forty ninethousandths; three hundred (units) and forty nine-thousandths. In dictating such numbers, it would be necessary to be still more explicit. 16. 4 lb. 6 oz. 12 pwt. 1872 pwt. Ans. £13 8s. 4d. x 12. pence. = = 1092 pwt.; 7 lb. 9 oz. 12 pwt. (£13 8s. 4d.) x 1872 ÷ 1092 = (canceling) If preferred, £ 13 8s. 4d. may be reduced to = 17. Total amount realized $22500. $20000 +$1500 +$1000 = A furnishes one-third of the $15000 capital, and is entitled to of $22500, or $7500. Having drawn $1500 already, he should receive $6000 additional. B's share $15000-$1000 = $14000. = 18. The gain on an article bought for 80% of its value and sold for 120% of its value, is 40% of its value. 40% is of the cost, 80%, so that the gain is 50%. per cent The words " occur so frequently in the foregoing as to confuse some children. Calling the value 100 x, the cost is 80 x and the selling price is 120 x, a gain of 40 x, which is of the cost, 80 x, or 50%. 19. $9 half-yearly, or $18 yearly, is the interest on the difference between $1200 and $750, or $450. The rate is 4%. 21. M does in a day; N, ; O,; together, ++ in 15+12+10_37 in 1 da. To do the whole work will 60 60 1 da., or The teacher should not neglect to have her pupils make an estimate of the answer of each problem before beginning work. They will find in doing this, that they can solve many of the problems without using the pencil. It will be found useful as an occasional class exercise to require each pupil to write on paper at a signal, his estimate of, say, ten problems similar to some of the foregoing. Anything that will cause a pupil to read carefully and understandingly before setting his pencil to paper, will by of great value to him in problem work. See Art. 981. 1086. 1. Let x = first cost of the goods. = = = 122.16; 24 x 12216; x=509; cost $509. The number of yards purchased = 32 × 32 = 1024; invoice price per yard = $509102449181. Cost of the goods, including duties, etc., = $509 + $122.16 + $40.96 = $672.12; total cost per yard, = $672.12÷102465188. 2. The amount paid $12500+ 9 months' interest on $3500+18 months' interest on $2600 + 28 months' interest on $2400. 3. At the end of 30 da., the provisions will last 1200 men 70 da. If half the men are then withdrawn, the remaining 600 will consume in 30 da. what 1200 men would use in 15 da., leaving 55 days' provisions for 1200 men. If the force is increased then by 900 men, there will be 1500 in the garrison. 55 days' provisions for 1200 men will last 1500 men 10% of 55 da. of 55 da. 44 da. Total time, 30 da. + 30 da. + 44 da. = 104 da. 5. of 4 of 25 = 15; 15 × 1 of 15 ÷ 1. 6. 97% of amount = $762742.50. 9. The tea cost 25¢ per lb. A gain of 15 = 60%. 1087. These exercises should be omitted if not required by the course of study. 3. The rate is x dollars per $1000 premium; on $1800, the premium The interest on $1800 for 60 days @ 9x I 6% 1% of $1800 $18. The equation becomes +1782 5 15.75; x 5 - 1.75. The minus sign indicates that it is a discount. Ans. 1088. 4. 10 5. Each face contains 1350 sq. in. +6 225 sq. in. Length = 1089. Another method of subdividing square C is here shown, Fig. 3. From each side of C, a right-angled triangle is cut, of the same dimensions as the original triangle m, leaving a small square X. In Fig. 4, is shown a rearrangement of these triangles, making a polygon equal in surface to the sum of the squares A and B, Fig. 5. 1091. 1. To find, divide by 4, placing each quotient figure one place to the right. Nothing should be written beyond what is shown in the Arithmetic. To find the interest, see Art. 983, 27. 2. 1% each quarter. In dividing by 100, the dividend is repeated, with each figure two places to the right. 3. 3% each half year. Multiply by 3, placing each figure of the product two places to the right. 1092. In some cities, the quotations of stocks give the price per share. A share whose par value is $50 and which sells for $48, is quoted in the New York papers as worth 96; i.e. 96% |